THE  LIBRARY 

OF 
THE  UNIVERSITY 

OF  CALIFORNIA 
LOS  ANGELES 


LECTURES 


ERRORS  OF  REFRACTION 


AND   THEIR 


CORRECTION  WITH  GLASSES 


DELIVERED   AT  THE 


NEW   YORK   POST-GRADUATE   MEDICAL  SCHOOL 


ILLUSTRATIVE   CASES   FROM   PRACTICE,  BOTH   PRIVATE   AND   CLINICAL 


BY 


FRANCIS   VALK,  M.D. 


1ECTURER   ON   THE   DISEASES    OF  THE   EYE,  NEW  YORK   POST-GRADUATE   MEDICAL  SCHOOL  ;   OPHTHAIv 
MOLOGIST  TO  THE   NEW   YORK  DISPENSARY  ;     FORMERLY    ASSISTANT  SURGEON,  MANHATTAN 
EYE  AND  EAR  HOSPITAL  ;   VISITING  OPHTHALMOLOGIST  TO  THE  RANDALL'S  ISLAND 
HOSPITALS  ;  ASSISTANT  TO  THE  CHAIR  OF  OPHTHALMOLOGY  AND  OTOL- 
OGY,   AND    ASSISTANT    DEMONSTRATOR     OF    ANATOMY,    AT 
THE    UNIVERSITY   OF  THE   CITY   OF   NEW   YORK 


NEW  YORK  AND  LONDON 

G.  P.  PUTNAM'S   SONS 

^\t  Jlmcherbocker  ^ress 
1889 


COPYRIGHT   BY 

FRANCIS  VALK,  M.D. 
1889 


Press  of 

G.  P.  PUTNAM'S  SONS 
NEW  YORK 


TO 

D.  B.  ST.  JOHN    ROOSA,  M.D.,  LL.D. 

PROFESSOR   OF    DISEASES   OF  THE   EYE   AND   EAR   IN   THE  NEW   YORK   POST-GRADUATB 

MEDICAL  SCHOOL  AND    HOSPITAL,  AND   PRESIDENT  OF  THE  FACULTY, 

MY  TEACHER  AT  THE   UNIVERSITY   OF  THE   CITY   OF   NEW 

YORK,   AND   CONSTANT  ADVISER   SINCE   THEN 

AND   TO 

WILLIAM    H.  FOX,  M.D. 

WASHINGTON,   D.    C. 
MY     BELOVED     FRIEND     AND    ASSISTANT 

THIS   WORK   IS  DEDICATED 

IN   RESPECTFUL    ADMIRATION    OF   THEIR   WORK   AS 
PHYSICIANS   AND   SURGEONS 


PREFACE. 

THESE  lectures  to  the  physicians  who  attended  the 
section  on  Diseases  of  the  Eye,  at  the  New  York  Post- 
Graduate  School,  having  been  received  by  them  with 
many  words  of  approval,  and  also  with  the  request  that  I 
would  publish  them,  are  my  reasons  for  now  offering  this 
work  upon  the  "  Errors  of  Refraction  "  to  the  profession. 
I  know  that  many  text-books  treat  this  subject  in  perhaps 
a  more  scientific  manner  than  it  is  here  presented,  but  I 
have  endeavored  to  make  this  work  as  simple  and  prac- 
tical as  possible. 

The  methods  of  testing  for  and  prescribing  glasses,  as 
herein  described,  are  so  simple  that  they  can  be  readily 
understood  even  by  one  who  is  not  familiar  with  the  science 
of  ophthalmology  ;  and  are  so  written  that  they  will  be  of 
service  in  the  hands  of  the  general  practitioner,  who  has 
too  little  time  to  devote  to  the  study  of  the  larger  works 
on  Refraction. 

I  believe  that  there  are  some  subjects  which  I  have 
discussed  that  will  also  be  of  value  to  the  specialist,  in 
the  work  of  correcting  the  errors  of  refraction  ;  as  in 
the  lectures  on  retinoscopy  and  astigmatism,  and  in  the 
diagnosis  of  refraction  with  the  ophthalmoscope. 

I  am  indebted  to  my  friend  and  teacher,  Prof.  D.  B. 
St.  John  Roosa,  for  many  of  the  practical  points  in  these 
lectures,  and  likewise  for  almost  all  my  early  teachings  on 
this  subject.  I  am  also  indebted  to  my  kind  friend,  Dr. 
W.  H.  Fox  (now  of  Washington,  D.  C.),  who  was  with 
me  during  the  years  of  1886  and  1887  at  the  Post-Graduate 


VI  PREFACE. 

School,  and  from  whom  I  received  many  valuable  sug- 
gestions in  regard  to  the  refraction  of  the  rays  of  light,  as 
they  pass  to  and  from  the  retina  of  the  human  eye.  It  is 
with  great  pleasure  that  I  thank  these  gentlemen  for  their 
ever  ready  assistance  to  me  in  the  past,  and  for  their  kind 
advice  and  counsel  in  the  preparation  of  this  work. 

I  also  acknowledge  the  assistance  I  have  received  from 
the  books  of  Prof.  E.  Landolt,  of  Paris,  and  also  to  Gus- 
tavus  Hartridge,  F.R.C.S.,  England,  whose  works  on  Re- 
fraction I  have  studied  with  benefit  to  myself,  and  from 
which  I  have  quoted  in  these  lectures. 

,  The  illustrations  and  diagrams  are  many  of  them  repro- 
ductions of  the  blackboard  drawings  that  I  have  been 
accustomed  to  use  in  illustrating  my  lectures  to  the  classes, 
and  I  am  sure  will  be,  in  this  connection,  of  service  to  the 
reader,  in  understanding  the  direction  of  the  rays  of  light 
as  they  pass  through,  and  are  refracted  by,  the  various 
media. 

Repetition  of  many  points  and  cases  has  been  neces- 
sary in  this  work  to  make  it  clearly  understood,  and  to 
impress  the  methods  of  examination  on  the  reader ;  and 
while  to  the  specialist  they  may  seem  very  unnecessary, 
yet  to  the  physician  who  is  beginning  the  study  of  the 
errors  of  refraction  I  am  sure  they  will  be  of  service. 

As  a  simple  and  at  the  same  time  complete  method 
for  the  diagnosis  and  correction  of  all  the  errors  of  refrac- 
tion, I  offer  this  monograph  to  the  general  profession. 

New  York,  1888. 


CONTENTS. 


FIRST    LECTURE 

FACE 

ANATOMY          

I-I7 

SECOND    LECTURE 

REFRACTION    ......... 

18-42 

THIRD    LECTURE 

EMMETROPIA    

43-56 

FOURTH    LECTURE 

HYPERMETROPIA       ........ 

57^7 

FIFTH    LECTURE 

MYOPIA    

68-78 

SIXTH    LECTURE 
OPHTHALMOSCOPY   ...... 

SEVENTH    LECTURE 
MUSCULAR    ASTHENOPIA  .... 

EIGHTH    LECTURE 
ASTIGMATISM  ....... 

NINTH    LECTURE 
RETINOSCOPY  ....... 

TENTH    LECTURE 
PRESBYOPIA       ....... 

ELEVENTH    LECTURE 
ILLUSTRATIVE   CASES         ..... 

INDEX 


79-112 

.  II3-I43 

.  144-174 

.  175-194 

.  195-206 

.  207-235 

.  237-241 


ILLUSTRATIONS  AND  DIAGRAMS. 


PLATE   i. — HORIZONTAL  SECTION  OF  THE  HUMAN  EYE.     (SOELBERG 

WELLS.) 
PLATE   2. — SECTION   OF   THE  EYE  CONCERNED  IN  ACCOMMODATION. 

(WELLS.) 

FIGURE  PAGE 

i. — A    VERTICAL    SECTION    OF    THE    EYEBALL.      ENLARGED. 

(AFTER  GRAY) 4 

2. — DIAGRAMMATIC   REPRESENTATION   OF  A  SECTION  OF   THE 

HUMAN  EYE  .........         5. 

3. — THE  OPHTHALMIC  ARTERY  AND  ITS  BRANCHES,  THE  ROOF 

OF  THE  ORBIT  HAVING  BEEN  REMOVED  ....         7 

4. — NERVES    OF    THE    ORBIT    AND    OPHTHALMIC    GANGLION. 

SIDE  VIEW       .        .         .......         8 

5. — MUSCLES  OF  THE  RIGHT  ORBIT     ......        9 

6. — THE  AXES  OF  ROTATION  OF  THE  EYEBALLS.     (AFTER  LAN- 
DOLT)      .         .        .         .         .        .         .        .         .        .11 

7. — SECTION  OF  THE  LENS,  ETC.:  SHOWING  THE  MECHANISM  OF 

ACCOMMODATION    .         .         .         .        .         .         .        .12 

8. — SECTION  THROUGH  THE  CILIARY  BODY  (EMMETROPIA)         .       13 

9. — SECTION  OF  CILIARY  BODY  (HYPERMETROPIA)      .        .         .13 

10. — SECTION  OF  CILIARY  BODY  (MYOPIA)   .....       13 

ii. — DIAGRAM  SHOWING  RAYS  PASSING  THROUGH  THE  DIOPTRIC 
MEDIA.  PARALLEL  AND  DIVERGENT  RAYS  HAVING  THE 
SAME  DIRECTION  AFTER  PASSING  THE  LENS,  BY  THE 

ACTION  OF  THE  CILIARY  MUSCLE 14 

12* — REFRACTION  OF  RAYS  OF  LIGHT  ......       20 

13. — ANGLES  OF  INCIDENCE  AND  REFRACTION      .         .         .         .21 

14. — SECTION  OF  A  PRISM  AND  DIFFERENT  LENSES       .         .        .23 
15. — REFRACTION  OF  A  PRISM,  WITH  THE  ANGLES  OF  INCIDENCE 

AND  REFRACTION    ........       25 

16. — CONVERGENCE  OF  Two  PRISMS  PLACED  BASE  TO  BASE  .  26 
17. — A  BI-CONVEX  LENS  AND  ITS  POSITIVE  FOCAL  POINT  .  .  27 
18. — PRINCIPAL  AND  SECONDARY  AXES,  WITH  THEIR  FOCAL 

POINTS    .  28- 


X  ILLUSTRATIONS  AND  DIAGRAMS, 

FIGURE  PAGE 

19. — THE  OPTICAL  CENTRE,  ETC.    (AFTER  LANDOLT)        .        .  30 
20. — A  Bi-CoxcAVE  LENS,  WITH  ITS  NEGATIVE  FOCAL  POINT     .  32 
21. — DIAGRAM  SHOWING  THE  ANGLE  OF  REFRACTION  IN  A  BI- 
CONVEX LENS          ........  33 

22. — THE  POSITIONS  OF  THE  MERIDIANS  OR  PLANES    ...  36 
23. — END   OF   CYLINDER,  FROM   WHICH  THE  CYLINDRIC  GLASS 

is  CUT 37 

24. — PLANES  OF  LIGHT  WITH  REFRACTION,  IN  THE  Two  PRINCI- 
PAL MERIDIANS  OF  A  CYLINDRIC  LENS.     B,  THE  AXIAL 

PLANE 38 

25. — THE  CONJUGATE  Foci  OF  A  BI-CONVEX  LENS.  THE  DOTTED 
LINES  SIMPLY  SHOW  THE  COURSE  OF  RAYS  IN  OTHER 

PARTS  OF  THE  LENS 45 

26. — THE  CONJUGATE  Foci  OF  THE  EYE  AND  ESTIMATION  OF 

THE  SIZE  OF  RETINAL  IMAGE 47 

-•7. — THE  VISUAL  ANGLE,  AS  FORMED  BY  SNELLEN'S  TEST-TYPES  48 

2-ja. — EMERSON'S  PERIMETER 52 

28. — DIAGRAM  OF  THE  HYPERMETROPIC  EYE       ....  58 
29. — DIAGRAM    OF    THE    MYOPIC    EYE    AND     THE     PUNCTUM 

REMOTUM 72 

30. — DIAGRAM  ILLUSTRATING  SPASM  OF  THE  ACCOMMODATION   .  77 

31. — CONJUGATE  FOCAL  POINTS  OF  A  BI-CONVEX  LENS       .         .  81 

32. — VALK'S  IMPROVEMENT  ON  LORING'S  OPHTHALMOSCOPE        .  83 
33. — ACTION  OF  A  CONVEX  LENS  ON  THE  EMERGENT  RAYS  OF 

HYPERMETROPIA 87 

34. — THE  MYOPIC  EYE,  ITS  EMERGENT  RAYS,  AND  THEIR  COR- 
RECTION WITH  THE  GLASS  F 89 

35. — THE  EMMETROPIC  PLANE  ;  ENTERING  RAYS,  Ah.         .         .  90 

36. — THE  HYPERMETROPIC  PLANE  ;  ENTERING  RAYS,  Ah.           .  91 

37. — THE  EMMETROPIC  PLANE  ;  EMERGENT  RAYS,  Ah.         .         .  91 

38. — THE  HYPERMETROPIC  PLANE  ;  EMERGENT  RAYS,  Ah.           .  91 

39. — THE  EMMETROPIC  PLANE  ;  ENTERING  RAYS,  Am.        .         .  94 

40. — THE  MYOPIC  PLANE  ;  ENTERING  RAYS,  Am.        ...  94 

41. — THE  EMMETROPIC  PLANE  ;  EMERGING  RAYS,  Am.        .        •  $95 

42. — THE  MYOPIC  PLANE  ;  EMERGING  RAYS,  Am.  95 

43. — THE  HYPERMETROPIC  PLANE  ;  ENTERING  RAYS,  Ahm.         .  99 
44. — THE  MYOPIC  PLANE  ;  ENTERING  RAYS,  Ahm.      .        .         .100 

45. — THE  HYPERMETROPIC  PLANE  ;  EMERGING  RAYS,  Ahm.        .  100 

46. — THE  MYOPIC  PLANE  ;  EMERGING  RAYS,  Ahm.      .         .         .  100 

47. RAYS  PASSING  FROM  THE  MYOPIC  TO  THE  HYPERMETROPIC 

EYE  ARE   PARALLEL   IN   THE   SAME   DEGREE   OF  RE- 
FRACTION          105 


ILLUSTRATIONS  AND  DIAGRAMS.  xi 

FIGURE  PACK 

48. — THE   CONVEX   GLASS   C  CORRECTS    THE    MYOPIA    WHEN 

EXAMINED  BY  THE  HYPERMETROPE  OF  SLIGHT  DEGREES,     105 
49. — THE  CONCAVE  GLASS  C  CORRECTS  THE  MYOPIA  OF   Low 

DEGREES  WHEN  EXAMINED  BY  A  MYOPE        .        .        .     106 

50. — (HARTRIDGE) 108 

51. — (HARTRIDGE) 108 

52. — (HARTRIDGE) 109 

53. — E  EMMETROPIC  EYE  ;  RAYS  ISSUING  PARALLEL  :  IMAGE 
FORMED  AT  THE  PRINCIPAL  Focus  OF  LENS,  NO  MATTER 
AT  WHAT  DISTANCE  THE  LENS  is  FROM  THE  EYE  .  .  109 

54. — LENS  AT  4  CM .no 

55. — LENS  AT  12  CM.;   H HYPERMETROPIC  EYE  ;  C  THE  CENTRE 
OF  THE  LENS  :    AB  IMAGE  ON  RETINA  ;    ab  PROJECTED 
IMAGE  ;     /3ac    THE    FINAL    IMAGE    FORMED    BY    THE 
OBJECTIVE       .         .         .         .         .         .         .         .         .no 

METHOD  OF  TESTING  THE  ANGLE  OF  STRABISMUS        .        .118 
DIAGRAM  SHOWING  POSITION  OF  MACULA  ;    CONVERGENT 

STRABISMUS     .         . .121 

58. — DIAGRAM  SHOWING  DIRECTION  OF  VISUAL  LINE  :  DIVER- 
GENT STRABISMUS  .  .  .  .  .  .  .  .122 

59. — THE  ANGLE  a  .         . 123 

60. — DIAGRAM  SHOWING  THE  ESTIMATION  OF  ANGLE  a  .  .  125 
61. — THE  PROJECTION  OF  THE  IMAGE  :  HOMONYMOUS  DIPLOPIA  .  128 
62. — THE  PROJECTION  OF  THE  IMAGE  :  CROSSED  DIPLOPIA  .  .  129 
63. — THE  ANGLE  OF  DEVIATION  AND  THE  ANGLE  OF  PRISM  .  132 
64. — ACTION  OF  PRISM  IN  HOMONYMOUS  DIPLOPIA  .  .  .  135 
65. — METHOD  OF  TESTING  THE  MUSCLES  WITH  PRISMS  .  .  137 
66. — DIAGRAM  SHOWING  THE  METRE  ANGLE  ....  139 

67. — ACTION  OF  DECENTRED  LENS 142 

68. — THE  PERIPHERAL  REFRACTION  OF  A  BI-CONVEX  LENS  .  142 
69. — THE  PERIPHERAL  REFRACTION  OF  A  BI-CONCAVE  LENS  .  143 

690. — PLACIDO'S  KERATOSCOPE 148 

70. — VERTICAL  PLANE,  COMPOUND  CYLINDRIC  LENS  .        .        .     151 
71. — HORIZONTAL  PLANE,  COMPOUND  CYLINDRIC  LENS       .         .151 
72. — COMPOUND  CYLINDRIC  LENS,  ILLUSTRATING  ASTIGMATISM 

(VERTICAL  PLANE)         .         .         .         .         .         .         .152 

73. — COMPOUND  CYLINDRIC  LENS,  ILLUSTRATING  ASTIGMATISM 

(HORIZONTAL  PLANE) 152 

74. — DIAGRAM  ILLUSTRATING  SIMPLE  ASTIGMATISM  .  facing  155 
75. — DIAGRAM  ILLUSTRATING  COMPOUND  ASTIGMATISM  156 

76. — DIAGRAM  ILLUSTRATING  MIXED  ASTIGMATISM    .  157 

77. — GREEN'S  TEST-CARD  FOR  ASTIGMATISM        .        .          .  162 


xii  ILLUSTRATIONS  AND  DIAGRAMS. 

FIGCRK  PACK 

78. — JAVEL'S  TEST-CARD  FOR  ASTIGMATISM         ....     163, 
79. — DIAGRAM  OF  VERTICAL  AND  HORIZONTAL  PLANES  IN  AS- 
TIGMATISM        fating     169 

80. — RETINOSCOPY  WITH  THE  CONCAVE  MIRROR  .  .  .176 
81. — RETINOSCOPY:  RAYS  FROM  MYOPIC  EYE  .  .  .  .177 
82. — RETINOSCOPY  WITH  THE  PLANE  MIRROR  .  .  .  .  179, 
83. — RETINOSCOPY  WITH  THE  PLANE  MIRROR  :  MYOPIA  .  .  182 
84. — RETINOSCOPY  :  EMERGENT  RAYS,  HYPERMETROPIA  .  .  186 
85. — RETINOSCOPY  :  EMERGENT  RAYS,  MYOPIA  .  .  .  .187 
86. — RETINOSCOPY  :  MYOPIA  OF  Low  DEGREES  ....  188. 
87. — DIAGRAM  SHOWING  APPARENT  DIRECTION  OF  THE  RETINAL 

REFLEX  IN  ASTIGMATISM  AT  45° 193 

88. — DIAGRAM  OF  ACCOMMODATION  (DONDERS)  .  .  .  .198 
89. — MEYROWITZ'  TRIAL-FRAME  FOR  GLASSES  ....  230 


rnei 


PI.ATK  i. — HORIZONTAL  SECTION  OF  THE  HUMAN  EYE.     (SOELBERO  WELLS.) 


(—Cornea. 

if — Anterior  Elastic  Lamina. 
,-f — Epithelium  of  the  Anterior  Surface  of  the 

Cornea. 
CD — Membrane  of  Descemet,  or  Posterior  Elastic 

Lamina 
CDE—  Epithelium  of  the  Posterior  Surface  of  the 

Cornea. 
5 — Sclerotic. 

sf — Tenon's    Capsule,    the     Connect  ive-Tissue 
Layer. 


sc — Conjunctiva,  and  its  Epithelium 
csl — Canal  of  Schlemm. 
Ck — Choroid. 

Cf> — Pigment  Layer  of  the  Choroid. 
PC — Ciliary  Processes. 

mci — Ciliary    Muscle,    Longitudinal    Fibres. 
/—Iris. 

ip — Pigment  Layer  of  the  Iris. 
i — Iritic  Angle. 


FIRST  LECTURE. 

ANATOMY. 

Orbits — Their  formation — Parts  contained  in — The  eyeballs — The  tunics — Imaginary 
points — The  globe  of  the  eye — Anterior  and  posterior  pole — Optic  axis — 
Equator  and  planes — Arteries  of — Optic  nerve — Nerves  of  motion — Sympathetic 
nerves — The  muscular  system — Centre  of  rotation — Primary  and  secondary  posi- 
tion— Ciliary  muscle — Cornea — Aqueous  humor — Crystalline  lens — Vitreous  body 
— Retina — Macula  lutea. 

GENTLEMEN  : — You  will  agree  with   me    in  the  fact,   • 
that  the  necessity  of  perfect  sight,  and  the  correct  ap- 
preciation of  all  the  objects  surrounding  us,  is  not  only 
absolutely  essential  to  our  happiness,  but  also  necessary 
for  our  success  in  life. 

Under  these  circumstances  the  study  of  the  visual 
apparatus  and  the  efficiency  of  the  organs  of  vision  will 
not  only  be  very  interesting,  but  also  a  study  that  will 
well  repay  you  in  the  work  of  your  professional  life. 

Now,  there  are  certain  parts  not  directly  connected 
with  vision  that  we  should  consider,  such  as  the  anatomy 
of  the  orbits  and  their  contents,  which  will  better  enable 
us  to  appreciate  the  blessings  of  sight.  We  will  also 
learn  how  perfect  in  their  action,  and  how  delicate  in  their 
mechanism,  are  the  eyeballs  and  their  muscular  system. 

Few  of  us  ever  realize,  when  we  pass  the  eye  over  the 
pages  of  our  books,  or  look  from  one  object  to  another, 
or  to  a  distance  and  then  near  at  hand,  the  changes  that 
take  place  in  the  mechanism  of  the  eyeball.  I  use  the 
word  mechanism  because  we  must  study  the  eyeball  as  an 
optical  instrument,  remembering  only  that  it  is  always 


2        LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

subject  to  the  changes  that  nature  sees  fit  to  impose. 
Although  the  eye  is  not  a  perfect  optical  instrument,  we 
must  admit  that  its  power  of  self-adjustment  to  rays  of 
light  from  any  luminous  point  is  far  more  perfect  and 
simple  than  that  of  any  instrument  that  has  been  devised 
by  human  ingenuity. 

I  shall  endeavor  to  treat  the  subject  of  vision  and  the 
errors  of  refraction,  not  from  a  scientific  point  of  view, 
but  shall  place  facts  before  you  in  such  a  simple  yet  com- 
plete manner  that  they  can  be  readily  understood  ;  I  will 
then  leave  the  subject  to  your  own  inclinations  and  to 
earnest  clinical  work.  You  may  learn  many  things  from 
our  various  excellent  writers,  but,  to  perfect  yourselves  in 
the  correct  detection  of  the  errors  of  refraction,  your  eye 
and  hand  must  become  accustomed  to  do  their  work, 
just  as  the  skill  of  the  artisan  is  shown  in  the  work  that 
he  performs. 

No  man  can  accustom  his  eye  to  the  detection  of  re- 
fraction with  the  ophthalmoscope  until  he  has  devoted 
many  hours  to  the  use  of  the  instrument.  Some  of  our 
best  ophthalmologists  will  differ  very  essentially  on  the 
degree  of  refraction,  when  they  estimate  it  with  the 
ophthalmoscope  :  this  I  have  known  to  occur  in  several 
instances. 

I  can  only  teach  you  the  manner  of  using  your  instru- 
ments and  the  method  by  which  you  will  obtain  certain 
results  ;  all  the  rest  I  must  leave  to  your  own  constant 
work  and  study. 

Let  us,  therefore,  look  at  the  eyeball  and  its  appen- 
dages from  an  anatomical  point,  and  consider  its  sur- 
roundings, or  the  parts  which  serve  to  protect  and  nourish 
the  eyeball ;  and  then  pass  on  to  the  parts  most  intimately 
concerned  in  refraction. 

The  eyeballs  rest  in  the  bony  orbits  situated  in  the 
anterior  portion  of  the  skull.  These  orbits  protect  them 


ANATOMY. 


from  external  violence  and  serve  to  form  points  of  attach- 
ment for  the  muscles  which  move  them,  and  the  tissues 
that  occupy  the  back  portion  of  the  orbits  form  a  cushion 
upon  which  the  eyeballs  rest.  These  orbits  are  situated 
on  each  side  of  the  median  line  and  are  shaped  like  a  four- 
sided  prism,  with  their  bases  outward.  The  inner  sides  of 
these  two  cavities  run  parallel,  with  the  ethmoid  bone  be- 
tween, while  their  axes  point  toward  each  other,  forming 
an  angle  of  about  42  degrees. 

They  are  about  if  inches  deep,  and  are  formed  by 
seven  cranial  bones,  three  of  which  are  common  to  both 
cavities  ;  the  roof  of  each  cavity,  slightly  concave,  is 
formed  by  the  orbital  plate  of  the  frontal  bone,  and  at 
the  apex  is  a  small  portion  of  the  lesser  wing  of  the 
sphenoid. 

The  floor  is  formed  partly  by  the  bones  from  the 
inner  wall,  except  in  front  by  a  portion  of  the  malar  bone, 
and  near  the  apex  by  a  part  of  the  palatal  and  superior 
maxillary  bone. 

The  median  or  inner  wall  is  formed  by  the  superior 
maxillary,  the  os  planum  of  the  ethmoid,  and  the  lateral 
surface  of  the  lachrymal  bone  ;  while  the  lateral  or  outer 
wall  of  the  orbit  is  principally  composed  of  the  greater  wing 
of  the  sphenoid  and  the  frontal  process  of  the  malar  bone. 

The  openings  into  these  two  cavities  are  four  in 
number.  The  largest,  lying  between  the  lateral  wall  and 
the  roof,  is  the  anterior  lacerated  foramen  or  sphenoidal 
fissure,  which  serves  for  the  passage  of  the  third,  fourth, 
sixth,  and  ophthalmic  division  of  the  fifth  nerves  and  also 
the  ophthalmic  vein.  At  the  apex  we  have  the  optic 
foramen,  a  funnel-shaped  passage  for  the  optic  nerve  and 
the  ophthalmic  artery,  while  at  the  inner  junction  of  the 
median  wall  and  the  roof  are  the  anterior  and  the  pos- 
terior ethmoidal  foramen  for  the  passage  of  the  ethmoidal 
vessels  and  nasal  nerve. 


LECTURES  ON  THE  ERRORS  OF  REFRACTION. 


These  two  bony  cavities  contain  within  their  walls  all 
the  various  tissues  that  exist  in  the  other  parts  of  the 
body,  as  we  have  connective  tissue,  adipose  and  muscular 
tissue,  cartilages,  veins,  arteries,  nerves,  lymphatics,  and 
various  tissues  peculiar  to  the  eyeball  and  not  found  in 
other  parts.  The  orbits  are  lined  by  a  layer  of  periosteum, 
which  forms  a  thick  tendinous  ring  around  the  optic 
foramen  for  the  attachment  of  the  muscles  which  move 
the  eyeballs  in  various  directions. 


ScUnttc 
Chorout 
Retina 


Tendon,  if  RCCTUf 


Ciliary  Mu*el» 
Ligament 


Hyaloid  M.*&***< 


Cavity       occupit 
ty   Vitr»»m*  Sum  our 


FIG.  i. — A  VERTICAL  SECTION  OF  THE  EYEBALL.      ENLARGED. — AFTER  GRAY. 

The  connective  and  adipose  tissues,  with  the  muscles, 
form  a  cushion  upon  which  the  eyeballs  rest,  protecting 
them  from  any  violence  from  without.  As  this  connective 
tissue  surrounds  the  eyeballs  and  muscles,  it  serves  as  a 
shield  and  protection,  while  holding  the  muscles  in  their 
proper  position.  The  anterior  portion,  covering  the  front 
of  the  eyeball,  is  called  Tenon's  capsule  ;  and  that  portion 
directly  beneath  the  conjunctiva,  the  subconjunctival  tis- 


ANATOMY.  5 

sue  ;  while  all  that  part  covering  the  posterior  portion  of 
the  eyeball,  is  called  Bonnet's  capsule. 

Lying  in  the  anterior  portion  of  the  orbits  'and  pro- 
tected by  the  eyelids,  while  they  are  held  in  position  by 
the  muscular  system,  are  the  essential  parts,  or  the  organs 
of  vision,  the  eyeballs.  These  are  in  the  form  of  a  sphere, 
with  the  segment  of  a  smaller  sphere  projecting  from 
their  anterior  surfaces. 


FIG.  2. — DIAGRAMMATIC  REPRESENTATION  OF  A  SECTION  OF  THE  HUMAN  EYE. 

The  eyeball  is  composed  of  three  tunics,  the  outer 
one  being  the  sclerotic,  with  the  cornea  anteriorly,  and 
beneath  this,  in  front,  is  the  uveal  tract,  consisting  of 
the  iris,  the  ciliary  body,  and  choroid,  or  tunica  vasculosa. 
These  parts  are  all  intimately  connected  ;  while  internal 
to  them  is  situated  the  most  sensitive  nervous  layer,  the 
retina.  Within  this  cavity,  formed  by  these  tunics,  we 
have  three  important  humors, — the  aqueous,  the  crystal- 
line lens,  and  the  vitreous  body. 


6        LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

Taking  the  eyeball  as  a  sphere,  we  fix  upon  its  surface 
certain  imaginary  points,  which  I  wish  you  to  remember. 
They  will  be  of  service  to  us  in  the  study  of  refraction,  and 
we  will  give  them  names  similar  to  corresponding  points 
upon  the  earth. 

We  have,  first,  the  anterior  pole,  at  the  centre  of  the 
cornea,  while  the  posterior  pole  lies  at  the  centre  of  the 
fundus,  or  back  part  of  the  eye  ;  and  an  imaginary  line  run- 
ning from  pole  to  pole  would  form  the  optic  axis.  But  you 
must  not  confound  this  with  the  visual  axis  or  line,  which 
passes  from  the  centre  of  the  macula  lutea,  or  yellow  spot, 
outward  through  the  cornea,  within,  and  a  little  above, 
the  anterior  pole,  directly  to  the  object  at  which  we  are 
looking.  This  line  crosses  the  optic  axis  at  the  nodal 
point,  which  lies  near  the  posterior  surface  of  the  crystal- 
line lens. 

If  we  now  draw  a  line  around  the  eyeball  at  its 
centre,  it  will  form  the  equator  of  the  eye,  and  the 
equatorial  plane  will  be  one  parallel  to  the  equator, 
dividing  the  eyeball  into  anterior  and  posterior  hemi- 
spheres. At  right  angles  to  this  equatorial  plane  we 
may  have  any  number  of  different  meridional  planes  at 
any  degree  on  the  arc  of  the  circle ;  their  axes  also 
coinciding  with  the  visual  axis.  If  you  will  remember 
that  the  refractive  power  of  the  eye  may  be  different  in 
each  one  of  these  planes,  it  will  assist  you  in  the  study  of 
refraction. 

The  arterial  system  of  the  eyeball  and  orbits  consists 
only  of  the  ophthalmic  artery  and  its  branches,  which  pro- 
ceed from  the  internal  carotid.  This  vessel  supplies  all 
the  tissues  of  the  orbits  and  eyeballs,  with  its  terminal 
branches  extending  outward  upon  the  face.  The  prin- 
cipal branches,  in  which  we  are  most  interested,  are  the 
ciliary  branches,  long  and  short,  and  the  central  artery  of 
the  retina,  the  artcria  ccntralis  ret  hue. 


ANATOMY.  7 

In  the  nervous  system  of  the  orbital  cavities  we  find 
the  nerves  of  motion  and  sensation,  chief  of  which  is  the 
optic  nerve,  passing  from  the  brain,  through  the  optic 
foramen,  to  the  eyeball.  This  is  surrounded  by  a  delicate 
nerve  sheath,  a  continuation  of  the  pia  mater.  As  this 
nerve  passes  forward  and  enters  the  sclerotic,  its  fibres 


Supra- 
orbital 


FIG.  3. — THE  OPHTHALMIC  ARTERY  AND  ITS  BRANCHES,  THE  ROOF  OF  THE 
ORBIT  HAVING  BEEN  REMOVED. 

pass  through  the  meshes  of  the  lamina  cribrosa,  a  short 
distance  to  the  inside  of  the  posterior  pole.  It  then  ex- 
pands in  all  directions,  spreading  out  over  the  internal 
surface  of  the  eye-ball,  forming  the  retina. 

The  nerves  of  motion  that  will  interest  us  in  the  study 
of  refraction  are  the  third,  fourth,  and  sixth,  which  have 
their  terminal  branches  in  the  various  muscles  that  con- 
trol the  movements  of  the  eyes.  The  third  or  motor 
oculi  supplies  all  the  muscles  within  the  orbit,  except  the 
superior  oblique,  which  is  supplied  by  the  fourth  or 
patheticus,  and  the  external  rectus,  supplied  by  the  sixth 
or  abducens.  This  third  nerve  also  sends  branches  to  the 


8        LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

muscle  of  accommodation,  and  to  the  sphincter  muscle  of 
the  iris,  though  these  fibres  are  supposed  to  have  a 
separate  origin  in  the  brain. 


Motor' 
Root 


FIG.  4. — NERVES  OF  THE  ORBIT  AND  OPHTHALMIC  GANGLION. — Sim  Vn:\v. 

The  sympathetic  branches  joining  the  different  nerves 
send  filaments  to  the  dilator  muscle  of  the  iris,  and  so  act 
antagonistically  to  the  filament  of  the  third  nerve. 

The  muscular  system  of  the  orbits  consists  of  six 
muscles,  which  move  the  eyeballs  in  any  direction  about 
a  common  centre  of  rotation,  directing  both  eyes  simul- 
taneously toward  any  object.  These  are  voluntary  mus- 
cles, being  under  the  control  of  the  will,  and  take  their 
origin  principally  from  the  tendinous  ring,  formed  by 
periosteum,  around  the  optic  foramen. 

The  four  recti  muscles  may  be  considered  almost  as 
one,  as  they  all  have  the  same  origin,  around  the  optic 
foramen.  These  pass  forward  in  the  sheaths  formed  by 
the  connective  tissue  of  the  periocular  space,  and  are  in- 


ANATOMY.  9 

serted  by  a  tendinous  expansion  into  the  sclerotic,  a  short 
distance  behind  the  limbus  of  the  cornea. 

Their  actions,  singly,  move  the  cornea  as  follows  : 
Upward,  by  the  superior  rectus  ;  downward,  by  the  infe- 
rior rectus  ;  outward,  by  the  external  rectus  ;  and  inward, 
by  the  internal  rectus.  The  combined  action  of  the  su- 
perior and  the  inferior  rectus  also  turns  the  eyeball  inward. 

The  remaining  muscles  are  called  the  superior  and  in- 
ferior oblique,  having  their  point  of  action  from  the  inner 
angle  of  the  orbits.  The  superior  oblique  arises  from  the 


FIG.  5. — MUSCLES  OF  THE  RIGHT  ORBIT. 

optic  foramen  on  the  inner  side,  and  as  it  passes  forward 
toward  the  upper  and  inner  angle  it  becomes  tendinous, 
passing  around  the  trochlear  process  of  the  frontal  bone  ; 
it  again  becomes  muscular,  and  then  passing  backward 
and  outward  beneath  the  superior  rectus,  it  is  inserted 
by  a  broad  and  flat  tendon  into  the  sclerotic,  between  the 
insertion  of  the  superior  and  the  external  rectus.  The 
action  of  this  muscle  rotates  the  eyeball  on  its  axis,  and 
turns  the  optic  axis  downward  and  outward. 

The  inferior  oblique  muscle,  arising  from  the  superior 


IO  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

maxillary  bone,  at  the  inner  portion  of  the  floor  of  the 
orbit,  and  passing  beneath  the  inferior  rectus,  outward 
and  backward,  is  inserted  into  the  sclerotic,  between  the 
entrance  of  the  optic  nerve  and  the  tendon  of  the  external 
rectus.  Its  action  serves  to  turn  the  cornea  upward  and 
outward,  and  at  the  same  time  rotate  the  eyeball  on  the 
optic  axis. 

This  muscular  system  will  turn  the  eyeball  in  almost 
any  direction  when  acting  singly  ;  while  the  action  of  any 
two  related  muscles  will  turn  the  eyeball  in  a  direction 
between  the  two  muscles,  as  in  the  action  of  the  superior 
and  the  internal  rectus  the  eyeball  will  move  directly  up- 
ward and  inward  ;  and  so  with  the  other  muscles.  It  is  al- 
ways a  difficult  matter  to  understand  and  appreciate  the 
different  directions  in  which  the  eyeball  is  moved  and  the 
action  of  the  various  muscles  concerned  ;  but  if*  we  will 
remember  the  common  centre  of  rotation  and  the  origin 
and  insertion  of  those  six  muscles,  their  action,  either 
combined  or  singly,  will  be  found  to  be  very  simple. 

When  the  muscular  system  is  at  rest  these  muscles, 
by  their  tonicity,  keep  the  eyeball  steady  against  the 
cushion  of  adipose  and  connective  tissue  in  the  orbit. 
The  optic  axes  are  directed  forward,  each  separate  muscle 
acting  in  antagonism  to  its  opposite  ;  then,  as  the  eyeball 
is  moved  in  any  direction,  it  turns  on  the  centre  of  rota- 
tion. This  point  is  situated  on  the  optic  axis,  about 
fourteen  millimetres  behind  the  cornea  and  ten  millimetres 
in  front  of  the  posterior  surface  of  the  sclerotic.  This  is 
the  point  of  intersection  of  the  various  axes  of  rotation 
of  the  eyeball. 

When  the  muscular  system  of  the  eyeballs  moves 
them  both  in  harmony,  it  is  called  the  associated  move- 
ment, and  the  visual  lines  are  parallel ;  while,  when  we 
use  the  muscle  of  accommodation,  we  have  the  accommo- 
dative movement. 


ANATOMY. 


II 


These  recti  muscles  are  antagonistic  when  the  action 
of  one  muscle  is  opposed  to  that  of  the  muscle  of  the 
opposite  side  ;  while  the  action  of  the  internal  rectus  is 
associated  with  the  action  of  the  ciliary  muscle  and  the 
iris,  in  the  act  of  accommodation. 

The  axis  of  rotation  of  the  superior  and  inferior  recti 
muscles  lies  in  the  horizontal  plane,  with  its  nasal  ex- 
tremity further  forward  than  the  'temporal  ;  so  that  the 
eyeball  is  carried  slightly  inward  by  the  combined  action 


FIG.  6. — THE  AXES  OF  ROTATION  OF  THE  EYEBALLS. — AFTER  LANDOLT. 

of  these  two  muscles,  as  their  origin  is  nearer  the  median 
line  than  the  centre  of  rotation.  The  internal  and  the 
external  rectus  are  directly  antagonistic,  and  move  the 
eyeball  on  a  vertical  axis  of  rotation.  The  axis  of  rotation 
of  the  superior  and  inferior  oblique  lying  in  the  horizontal 
plane  forms  an  angle  of  38  degrees  with  the  line  of 
fixation,  or  the  optic  axis  when  at  rest. 

When  we  have  these  muscles  in  a  state  of  tension,  the 
head  erect,  the  horizontal  and  vertical  meridians  in  their 


12 


LECTURES  ON  THE  ERRORS  OF  REFRACTION. 


proper  positions,  and  the  optic  axes  directed  forward,  the 
eyes  are  in  the  primary  position  ;  while  any  deviation  from 
this  is  called  a  secondary  position.  And  in  all  cases, 
whether  primary  or  secondary,  unless  there  should  be 
some  pathological  condition,  the  eyeballs  when  in  use 
are  so  directed  that  direct  rays  of  light  fall  upon  the  mac- 
ula lutea  of  each  eye. 

Within  the  eyeball  we  have  a  very  important  muscle, 
the  ciliary,  whose  action  controls  our  vision  for  all  points 
nearer  than  infinity.  This  muscle  arises  from  the  corneo- 


FIG.    7. — SECTION   OF  THE   LENS,   ETC.:   SHOWING  THE  MECHANISM   OF  ACCOM- 
MODATION. 

The  left  side  .of  the  figure  (F)  shows  the  lens  adapted  to  vision  at  infinite  dis- 
tances ;  the  right  side  of  the  figure  (X)  shows  the  lens  adapted  to  the  vision 
of  near  objects,  the  ciliary  muscle  being  contracted  and  the  suspensory  ligament  of 
the  lens  consequently  relaxed. 

scleral  junction,  at  the  inner  side  of  the  canal  of  Schlemm, 
by  a  tendinous  origin.  It  is  composed  of  two  sets  of 
fibres  ;  the  radiate,  which  are  inserted  into  the  ciliary  pro- 
cesses ;  and  the  circular,  or  circular  ciliary,  ligament. 
These  fibres  are  on  the  inner  side,  and  pass  around  and 
within  the  zone  of  the  ciliary  processes.  As  regards  the 
action  of  this  most  important  muscle,  I  think  the  de- 
scription in  Flint's  "Physiology"  about  the  best,  which 
says:  "When  this  muscle  contracts,  the  choroid  is  drawn 
forward,  with,  probably,  a  slightly  spiral  motion  on  the 


ANATOMY. 


FIG.  8. — SECTION  THROUGH  THE  CILIARY  BODY  (EMMETROPIA). 
Showing  the  ciliary  muscle :  a,   choroid  ;  6,  radiating  fibres  of  ciliary  muscle — the 
small  group  of  circular  fibres  are  seen  lying  to  the  median  side  of  the  radiating  ;  d,  a 
transverse  section  of  a  blood-vessel  ;  f,  the  uvea  of  the  iris  ;  g,  the  pigment  layer  of 
the  ciliary  body  ;   h,  the  spaces  of  Fontana  (rendered  too  conspicuous). 


FIG.  9. — SECTION  OF  CILIARY  BODY. 

Showing  the  hypertrophy  of  the  circular  fibres  of  the  ciliary  muscle  in  hypermetropia  : 
i,  The  radiate  fibres  of  the  ciliary  muscle  ;  2,  the  sclera  ;  4,  the  circular  fibres  of  the 
ciliary  muscle  ;  5,  the  iris  ;  6,  the  canal  of  Schlemm. 


FIG.  10. — SECTION  OF  CILIARY  BODY. 

Showing  absence  of  the  circular  fibres  of  the  ciliary  muscle  in  myopia  :  I,  The  radi- 
ate fibres  ;  2,  the  sclera  ;  3,  the  section  of  a  vessel  ;  4,  the  ciliary  processes  :  5,  the 
iris. 


14       U-'.CTURES  ON  THE  ERRORS  OF  REFRACTION. 

lens.  The  contents  of  the  globe,  situated  posteriorly  to- 
the  lens,  are  compressed,  and  the  suspensory  ligament  is 
relaxed.  The  lens  itself,  the  compressing  and  flattening 
action  of  the  suspensory  ligament  being  diminished,  be- 
comes thicker  and  more  convexed,  by  virtue  of  its  own 
elasticity." 

As  by  this  action  of  the  ciliary  muscle  the  lens  is 
rendered  more  convex  on  its  anterior  surface,  increasing 
its  power  to  bend  rays  of  light,  you  will  understand  that 
the  divergent  rays  from  objects  within  infinity  are  exactly 
brought  to  a  focus  upon  the  retina.  It  is  by  the  action  of 
the  ciliary  muscle  that  the  mechanism  of  accommodation 
is  accomplished,  and  all  the  requirements  of  vision  are 
adjusted  perfectly. 


FIG.  ii. — DIAGRAM  SHOWING  RAYS  PASSING  THROTGH  THE  DIOPTRIC  MKDIA. 
PARALLEL  AND  DIVERGENT  RAYS  HAVING  THE  SAMK  DIRECTION  AFTER  I-A.^MM; 
THE  LENS,  BY  THE  ACTION  OF  THE  CILIARY  MUSCLE. 

In  the  above  diagram  the  parallel  rays  are  shown  en- 
tering the  eye,  a  a  a  a,  refracted  by  the  dioptric  apparatus. 
With  the  eye  at  rest  and  the  anterior  surface  of  the  lens 


ANATOMY.  15 

at  e,  they  will  then  focus  at  the  point  c,  on  the  retina ; 
but  when  they  come  from  a  nearer  point,  and  have  a 
divergent  direction  as  b  b  b  b,  we  find  the  anterior  surface 
of  the  lens  at  d,  by  the  action  of  the  ciliary  muscle 
increasing  the  power  of  refraction.  These  rays  take  the 
same  course  from  the  lens  to  the  retina. 

The  action  of  the  ciliary  muscle  is  controlled  by  the 
ciliary  nerves,  which  pass  from  their  origin  in  the  ciliary 
ganglion  through  the  posterior  portion  of  the  sclerotic. 

We  will  now  pass  to  the  anatomical  parts  of  the  globe 
that  are  directly  concerned  in  the  act  of  vision,  as  the  rays 
of  light  are  refracted.  We  consider  that  when  these  rays 
come  from  an  object  more  than  twenty  feet  distant  they 
are  practically  parallel,  and  first  impinge  upon  the  corneal 
tissue,  passing  through  its  five  layers,  as  follows  :  First, 
the  epithelial  coat,  a  continuation  of  the  conjunctival 
epithelium  ;  second,  the  anterior  elastic  lamina  ;  third,  the 
true  corneal  tissue  ;  fourth,  the  posterior  elastic  lamina  ; 
and  fifth,  the  posterior  epithelium,  or  Descemefs  membrane. 
These  five  layers  form  a  clear  homogeneous  membrane 
that,  from  its  convex  anterior  surface,  has  great  power  in 
bending  or  refracting  the  rays  of  light,  which,  as  they  pass 
through  the  cornea,  would  again  become  almost  parallel, 
except  for  the  next  refractive  media,  the  aqueous  humor. 
This  is  a  clear  watery  fluid,  which  fills  the  spaces  of  the 
anterior  and  posterior  chambers  between  the  cornea  and 
lens,  and  whose  power  of  refraction  is  almost  the  same  as 
that  of  the  cornea. 

Passing  backward  we  now  come  to  the  crystalline 
lens,  lying  just  posterior  to  the  pupil  of  the  iris,  and 
suspended  between  the  aqueous  and  vitreous  humors  by 
the  zone  of  Zinn,  or  suspensory  ligament.  This  ligament 
is  attached  to  the  anterior  capsule  of  the  lens,  being  a 
continuation  of  the  anterior  portion  of  the  hyaloid  mem- 
brane ;  which  membrane  is  also  blended  with  the  ciliary 


1 6  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

muscle  at  the  ciliary  processes,  and  by  this  means  controls 
the  action  of  the  lens  in  the  act  of  accommodation.  The 
lens  is  a  bi-convex,  transparent  body,  inclosed  within  its 
own  capsule,  and  surrounded  at  its  periphery  by  the  canal 
of  Petit,  which  lies  between  the  layers  of  the  hyaloid 
membrane. 

The  lens  measures  about  one  third  of  an  inch  (eight 
mm.)  from  side  to  side,  and  one  fifth  of  an  inch  thick.  It 
is  less  convex  in  front  than  behind,  except  when  the 
ciliary  muscle  contracts  in  accommodation,  when  its  an- 
terior surface  projects  into  the  anterior  chamber,  thereby 
increasing  its  refractive  power  and  bending  the  rays  to  an 
exact  focus  upon  the  retina. 

Lastly,  in  our  dioptric  or  refractive  media  we  have 
the  vitreous  body,  which  completely  fills  the  rest  of  the 
globe  of  the  eye.  It  consists  of  a  jelly-like,  transparent 
structure,  with  a  central  depression  in  front,  the  hyaloid 
fossa  for  the  crystalline  lens,  and  is  surrounded  by  the 
hyaloid  membrane,  the  anterior  portion  of  which  you  will 
remember,  divides  into  two  delicate  layers  on  each  side 
of  the  canal  of  Petit. 

The  rays  of  light  still  further  refracted  by  the  vitreous 
body,  now  strike  upon  the  retina,  and,  being  brought  to 
complete  focus,  there  produce  an  exact  inverted  image  of 
the  object  from  which  the  rays  proceed.  The  retina  is  a 
continuation  of  the  optic  nerve,  expanding  outward  in  all 
directions,  from  the  nerve  entrance  to  all  parts  of  the 
inner  surface  of  the  globe,  until  it  ends  at  the  ora  serrata, 
near  the  ciliary  processes.  It  is  transparent,  grayish  in 
color,  about  one  seventy-fifth  of  an  inch  thick,  and  gradu- 
ally tapers  until,  at  its  periphery,  it  is  about  one  two- 
hundredth  of  an  inch.  It  is  composed  of  nervous  elements 
and  connective  tissue  ;  it  receives  all  the  visual  impres- 
sions, and  through  its  nervous  power  conveys  them  to  the 
brain. 


ANATOMY.  17 

Before  closing  this  lecture  let  me  call  your  attention 
to  the  macula  hitea,  or  the  yellow  spot  of  the  retina,  lying 
near  the  posterior  pole  and  between  that  point  and  the 
entrance  of  the  optic  nerve.  It  presents  more  by  its 
negative  characters  than  by  any  positive  ones.  As  a  rule, 
you  will  find  no  distinct  marks  of  its  location  in  the 
normal  eye,  except  a  slight  deepening  of  the  retinal  pig- 
ment and  the  absence  of  blood-vessels  :  these  latter  all 
pass  around  it.  In  looking  for  this  spot  with  the  ophthal- 
moscope you  will  find  it  at  the  temporal  side  of  the  nerve 
entrance,  and  about  two  diameters  of  the  nerve  distant, 
on  a  line  with  the  lower  border  of  the  optic  nerve.  In 
some  cases  where  we  have  normal  vision  the  fovea  cen- 
tralis,  or  central  depression  of  the  macula  lutea,  is  well 
marked  as  a  small,  irregular  spot,  due,  no  doubt,  to  a 
large  excess  of  pigment.  At  this  important  point  in  the 
retina,  where  all  the  rays  of  our  direct  vision  focus,  the 
retina  itself  is  very  thin,  and  only  composed  of  the  rods 
and  cones,  the  essential  nervous  elements. 

It  is  at  this  point  that  the  visual  axis  ends  ;  it  is  also 
the  point  of  perfect  vision.  As  we  recede  from  it  the  sen- 
sibility of  the  retina  becomes  less  and  less,  until  we  reach 
the  ora  serrata,  at  the  extreme  periphery.  The  retina 
extends  so  far  forward  that  rays  of  light  passing  in  a 
straight  line  which  can  enter  the  eye  must  strike  upon  it, 
there  producing  a  more  or  less  distinct  image,  according 
to  the  distance  from  the  macula  lutea,  or  point  of  perfect 
vision. 


SECOND  LECTURE. 

REFRACTION. 

-Dioptric  apparatus — Infinity — Refraction  of  light — Angle  of  incidence — Angle  of 
refraction — Prisms — Lenses — The  bi-convex  lens — Principal  and  secondary  axes 
— The  bi-concave  lens — The  negative  focal  point — Meniscus  and  concavo-convex 
— Dioptric  media — Their  index  of  refraction — The  iris — Its  purpose — Cylindric 

•  lenses — The  two  principal  planes — Metric  system — The  dioptry — Tables  of  com- 
parison— To  change  to  inches. 

GENTLEMEN  :  As  we  have  studied  the  anatomical  por- 
tions of  the  globe  of  the  eye  that  are  essential  to  vision, 
let  us  now  study  how  these  anatomical  parts  act  in 
bringing  the  rays  of  light  to  a  perfect  focus  on  the  sensi- 
tive retina,  and  what  is  the  position  of  the  image  there 
formed. 

No  very  considerable  time  has  elapsed  since  we  have 
mastered  the  subject  of  refraction,  although  glasses  were 
first  worn,  for  presbyopia,  in  the  thirteenth  century.  Nor 
•did  we  comprehend  how  the  rays  of  light  were  refracted 
until  DONDERS  published  his  classical  work,  giving  to  the 
world  a  complete  exposition  of  refraction  in  all  the  grades 
of  ametropia,  and  suggested  the  ready  means  of  correction. 

It  is  HELMHOLTZ  to  whom  we  are  indebted  for  the 
knowledge  of  the  exact  refraction  of  the  eye,  as,  by  his 
instrument,  the  ophthalmometer,  we  learn  the  radii  of 
curvature  of  the  cornea  and  lens,  with  the  indices  of  re- 
fraction of  the  various  media  through  which  a  ray  of  light 
passes  to  the  retina. 

We  consider  the  refractive  parts  of  the  eyeball  as  the 
cornea,  aqueous  humor,  crystalline  lens,  and  vitreous 

18 


REFRACTION.  19 

body.  These  taken  collectively,  are  called  the  dioptric 
media  ;  which  refer  to  those  portions  of  the  eyeball  through 
which  rays  of  light  pass  that  enable  us  to  see,  having  no 
reference  to  the  dioptry. 

All  objects  send  off  rays  of  light  in  every  direction, 
which  are  direct  or  reflected.  These  rays  pass  in  straight 
lines,  unless  they  meet  some  substance,  that  will  either 
reflect  and  send  them  backward,  or  refract  and  bend 
them  in  their  course.  This  refraction  simply  changes 
their  direction,  when  they  pass  on  in  straight  lines  again. 

In  the  study  of  refraction  we  consider  that  all  rays  of 
light,  either  direct  or  refracted,  travel  in  parallel  paths 
when  they  come  from  a  distance  of  twenty  feet  or  more ; 
this  distance  is  called  infinity,  while  all  rays  that  come 
from  a  nearer  point  than  infinity  are  divergent.  Theo- 
retically, all  rays  of  light  are  divergent,  as  they  come 
from  a  minute  luminous  point ;  but,  practically,  for  any 
distance  beyond  twenty  feet  they  are  considered  parallel. 

Thus  .you  will  understand  that  when  we  look  at  an 
object,  such  as  the  usual  test  letters,  placed  at  a  distance  of 
twenty  feet,  the  rays  of  light  reflected  from  the  letters  will 
enter  the  eye  parallel,  and  all  those  coming  from  a  nearer 
point  than  twenty  feet,  up  to  the  nearest  one  of  distinct 
vision,  enter  divergent ;  and  that  the  nearer  to  the  eye  we 
place  the  object  or  letters,  the  more  divergent  are  the  rays 
of  light. 

Having  just  said  that  all  rays  pass  in  straight  lines 
unless  refracted  or  bent,  we  will  now  consider  how  a  ray 
of  light  is  so  affected,  or,  in  other  words,  the  subject  of  re- 
fraction of  light.  The  meaning  of  the  word  REFRACTION  is 
bending  back,  as  you  will  notice  the  rays  are  so  bent  by 
passing  through  certain  media,  as  water  or  glass. 

To  illustrate  this  subject  plainly,  we  take  a  square  box 
as  shown  in  fig.  12,  M,  N,  P,  O.  If  we  put  a  small  hole 
in  one  side  of  the  box,  as  at  a,  and  allow  a  ray  or  beam 


20 


LECTURES  ON  THE  £AA'OXS  OF  REFRACTION. 


of  light  to  pass  through  this  hole,  it  will  strike  the  bottom 
of  the  box  at  C.  Now  fill  the  box  with  water  up  to  the 
line  sr  and  you  will  see  the  ray  strike  at  the  point  D  ; 
making  it  very  evident  that  the  ray  of  light,  after  striking 
the  surface  of  the  water  at  B,  instead  of  passing  directly 
onward  to  C,  is  bent  or  refracted  backward  to  D. 

If  in  place  of  water  we  use  some  denser  medium,  such 
as  glass,  we  will  now  find  that  the  ray  aB  is  still  further 
refracted,  and  strikes  the  bottom  of  the  box  at  x.  Hence 
we  may  conclude  that  when  a  ray  of  light,  passing 
through  the  air,  falls  in  an  oblique  direction  upon  the 
surface  of  a  liquid  or  solid  body,  through  which  light  can 


K, 


,v 


FIG.  12. — REFRACTION  OF  RAYS  OF  LIGHT. 

pass,  it  is  refracted ;  and  by  different  .bodies   in  different 
degrees,  according  to  their  density. 

Now  take  a  bright  piece  of  money  and  place  it  in  the 
same  vessel,  when  empty,  at  the  point  C,  and  place  the 
eye  at  a.  The  coin  can  be  distinctly  seen.  Fill  the 
vessel  again  with  water  to  the  line  sr,  and  the  coin 
is  no  longer  visible  at  C,  but  must  be  placed  at  the  point/?. 
Hence  it  follows  that  the  rays  of  light  that  proceed  from 
D  take  exactly  the  same  course,  or  are  refracted,  when 
they  leave  the  water,  to  a,  as  they  did  when  the  rays 
passed  from  a  to  D.  So  we  may  again  conclude,  that 
when  a  ray  of  light  passes  through  a  liquid  or  trans- 


REFRACTION. 


21 


parent  solid  body  obliquely  to  its  surface,  and  enters  the 
air,  it  is  refracted  according  to  the  medium  through  which 
it  passes,  unless  the  direction  of  the  rays  should  be 
beyond  the  limit  angle,  when  they  would  simply  be  re- 
flected by  the  surface  of  the  water,  and  would  not  pass 
outward  so  as  to  be  refracted.  We  have  now  explained 
the  directions  in  which  rays  of  light  proceed  when  passing 
from  a  rare  medium,  such  as  the  air,  into  a  dense  medium, 
as  water  or  glass  ;  and  also  from  a  dense  to  a  rare  me- 
dium. Let  us  consider  the  rule  or  method  by  which  we 
can  calculate  the  direction  in  which  rays  are  refracted 
when  passing  through  different  media. 


FIG.  13. — ANGLES  OF  INCIDENCE  AND  REFRACTION. 

For  this  purpose  draw  a  circle,  as  D  F  E  G,  then  draw 
two  lines  across  the  circle  at  right  angles,  as  D  to  E 
and  F  to  G,  making  two  diameters,  one  perpendicular  to 
FG.  Now  if  a  ray  of  light  passes  from  A  to  C,  and  at 
the  point  C  falls  upon  a  denser  medium  in  an  oblique  di- 
rection, it  will  be  refracted  to  the  point  B ;  while  another 
ray,  passing  from  D  to  C,  and  falling  perpendicularly  to 
the  surface,  will  pass  directly  to  E.  Thus  we  see  that  a 
ray  passing  directly  through  a  dense  medium  perpendicu- 
lar to  its  surface,  is  not  refracted,  and  that  the  line  DC 
is  the  normal  of  the  surface  at  C. 


22  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

Now  the  angle  formed  by  the  lines  A,  C,  and  D  is 
called  the  angle  of  incidence,  and  the  angle  Bt  C,  and  E  is 
called  the  angle  of  refraction  ;  and  if  we  compare  the  dis- 
tance of  the  line  A  to  x  with  that  of  the  line  B  to^j',  we 
will  find  their  lengths  are  in  the  proportion  of  i^  to  i,  or, 
strictly  speaking,  if  the  denser  medium  be  water,  1.336  to 
i  ;  and  still  further  that  the  line  A  to  x  is  called  the  sine 
of  the  angle  of  incidence,  and  the  line  B  to  y  the  sine  of 
the  angle  of  refraction.  You  will  also  notice  that  the  line 
CB  is  bent  toward  the  perpendicular  line  DE,  and  that, 
as  shown  in  the  diagram,  the  proportion  of  the  sine  of  the 
angle  of  incidence  is  to  the  sine  of  the  angle  of  refraction 
as  4  to  3  when  the  refracting  body  is  water. 

If  we  now  reverse  the  direction  of  the  ray,  allowing  it 
to  pass  through  the  dense  medium  from  B  to  C,  we  will 
find  that,  as  it  enters  the  rarer  medium,  or  the  air,  it 
is  refracted  in  the  direction  C  to  A,  or  away  from  the 
perpendicular  line  DE.  Thus  we  have  this  cardinal 
rule  :  that  when  a  ray  of  light  passes  obliquely  from  a 
lighter  or  rare  medium  to  a  dense  medium,  it  is  bent  tow- 
ard the  perpendicular ;  that,  when  passing  from  a  dense 
medium  to  a  lighter  one,  it  is  bent  from  the  perpendicu- 
lar, and  that,  when  it  passes  perpendicularly  to  the  sur- 
face, coincident  with  the  normal,  it  is  not  refracted. 

When  water  is  the  refracting  medium,  the  sine  of  the 
angle  of  incidence  is  to  the  sine  of  the  angle  of  refrao- 
tion  as  i^  is  to  i,  or  1.336  to  i,  (this  number  is  called 
its  index  of  refraction,  or  refractive  power),  while  that 
of  other  media,  as  glass,  which  is  generally  used  for 
optical  purposes,  is  about  1.5,  though  it  may  vary  between 
1.526  to  1.534  ;  and  the  sines  of  the  angles  when  pass- 
ing through  glass  will  be  about  as  1.5  to  i.  We  find 
that  the  refractive  index  of  the  dioptric  media  will  vary,  as 
it  will  be  different  in  the  cornea,  aqueous,  lens,  and  vitre- 
ous body,  according  to  their  physiological  density. 


REFRACTION, 


The  substance  which  is  used  for  the  refraction  of  rays 
of  light,  as  applied  to  our  study,  is  flint  glass.  This  solid 
medium  is  shaped  in  various  forms,  their  surfaces  being 
sections  of  a  sphere,  with  that  of  a  prism  as  abase.  Now, 
if  a  section  be  made  through  the  centre  of  the  different 
varieties  of  glasses  used  in  correction  of  refraction,  they 
will  appear  as  illustrated  in  fig.  14. 

A.  The  section  of  a  prism,  having  two  plain  surfaces 
inclining  toward  each  other,  and  a  base. 

B.  A    double    convex  lens,   bounded    by  two  convex 
spherical  surfaces,  whose  centres  of  curvature  are  on  op- 


a 


FIG.  14. — SECTION  OF  A  PRISM  AND  DIFFERENT  LENSES. 

posite  sides  to  their  curved  surfaces,  and  which  is  equally 
convex  on  both  sides. 

C.  A  plano-convex  lens,  bounded  by  a  plane  surface 
on  one  side  and  a  convex  on  the  opposite. 

D.  A  double  concave  lens,  bounded  by   two  concave 
surfaces,  whose  centres  of  curvature  are  on  the  same  sides 
of  the  lens. 

E.  A  plano-concave  lens,  bounded  by  a  plane  surface 
on  one  side  and  a  concave  on  the  opposite. 

F.  A  meniscus  lens,  bounded  by  a  concave  and  a  con- 
vex surface,  the  convex  having  the  shortest  radius  of  cur- 


24  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

vature,  which  two  surfaces  will  meet  if  continued,  as 
shown  at  a. 

G.  A  concavo-convex  lens,  bounded  by  a  concave 
and  a  convex  surface,  the  concave  having  the  shortest 
radius  :  these  two  surfaces  will  not  meet  if  continued. 

The  principal  axes  of  these  various  lenses  will  be  a 
line  drawn  through  their  centres,  at  right  angles  to  their 
plane  surfaces  ;  and  all  rays  passing  perpendicularly  to  the 
plane  of  the  point  of  contact  will  not  be  refracted,  but 
pass  directly  through. 

A  ray  of  light  passing  parallel  to  the  axis  of  any  of 
these  lenses,  and  striking  at  some  other  point,  must  fall 
obliquely  upon  the  surface,  and  the  lens  at  the  point  of 
contact  will  present  the  surface  of  one  of  the  sides  of  a 
prism.  The  ray  will  then  be  refracted,  the  same  as  when 
passing  through  a  prism  of  the  same  angle. 

We  will  now  study  how  the  rays  are  refracted  when 
passing  through  a  prism  of  flint  glass  whose  index  of 
refraction  is  1.5.  Here  we  must  remember  our  rule  :  that 
the  sine  of  the  angle  of  incidence  will  be  to  the  sine  of 
the  angle  of  refraction  as  r.5  is  to  i  ;  and  that,  when 
passing  from  the  glass  medium  to  that  of  air,  the  propor- 
tion will  be  exactly  reversed. 

A  ray  of  light  refracted  when  passing  through  a  prism 
is  the  basis  of  action  in  all  lenses,  which  are  practically 
composed  of  prisms.  The  course  of  a  ray  of  light  as  it 
passes  through  an  ordinary  triangular  prism,  with  the  base 
downward,  I  will  show  you  in  this  diagram.  (See  fig.  15.) 

As  the  ordinary  flint  glass  has  an  index  of  refraction 
of  about  1.525,  we  will  use  that  sum  in  our  calculations, 
according  to  our  rule  for  the  refraction  of  rays ;  remem- 
bering that,  to  be  refracted,  a  ray  of  light  must  strike  the 
surface  obliquely.  We  will  suppose  that  a  ray  passing 
from  A,  and  striking  the  side  of  the  prism  at  C,  is  re- 
fracted to  E.  Thus,  if  we  draw  a  circle  at  C,  and  erect  a 


REFRACTION.  2$ 

line  perpendicular  to  the  surface,  passing  through  C,  from 
P  to  Q,  we  will  find  that  the  sine  AD,  of  the  angle  of 
incidence,  is  to  the  sine  EF,  of  the  angle  of  refraction, 
as  1.525  is  to  i. 

Then,  as  the  ray  passes  from  the  prism,  we  find  that  it 
takes  the  direction  of  £',  being  bent  from  the  perpendic- 
ular. We  draw  the  circle  at  C,  and  erect  a  perpendicular, 
P  to  Q,  and  now  we  find  that  the  sine  A'D',  of  the  angle 
of  incidence,  is  to  the  sine  E'F ',  of  the  angle  of  refrac- 


FIG  15. — REFRACTION  OF  A  PRISM,  WITH  THE  ANGLES  OF  INCIDENCE  AND 

REFRACTION. 

tion,  as  i  is  to  1.525,  which  proves  our  simple  rule  that, 
when  a  ray  of  light  passes  from  a  lighter  to  a  denser 
medium,  it  is  bent  toward  the  perpendicular,  and  that 
when  passing  from  a  dense  to  a  lighter  medium,  it  is  bent 
from  the  perpendicular,  according  to  the  index  of  refrac- 
tion of  the  substance  through  which  it  passes. 

You  will  therefore  notice  that  a  ray  of  light  must  strike 
the  surface  obliquely,  when  it  will  be  refracted  according 
to  the  index  of  refraction  ;  that  the  ray  that  passes  in  a 


26  LECTURES  ON  THE   ERRORS  OF  REFRACTIOX. 

line  with  the  perpendicular  will  not  be  refracted,  as  it 
cannot  be  bent  toward,  or  from,  a  line  with  which  it  is 
coincident,  and  that  consequently  it  will  undergo  no  devi- 
ation. 

As  these  rays  are  consequently  bent  toward  the  base 
of  the  prism,  you  will  understand  the  laws  of  refraction 
when  rays  pass  through  curved  surfaces,  such  as  the  dif- 
rerent  lenses,  which  practically  consist  of  two  prisms 
placed  in  different  positions. 


FIG.  16. — CONVERGENCE  OF  TWO  PRISMS  PLACED  BASE  TO  BASE. 

The  first  lens  in  our  series,  the  bi-convex,  we  can  rep- 
resent by  two  prisms  placed  base  to  base.  Now,  according 
to  fig.  1 6,  you  will  see  that  the  parallel  rays  of  light  P, 
P,  P,  P,  P,  as  they  strike  the  surface  of  the  prisms  A,  B, 
are  bent  toward  their  bases,  and  as  they  pass  from  the 
prism  are  still  farther  bent  in  the  same  direction.  The 
central  line  represents  the  axis,  while  the  dotted  short 
lines  represent  the  perpendiculars  at  the  points  of  contact 
for  the  rays.  As  these  rays  are  refracted  after  passing 
through  the  prism,  they  must  meet  at  a  point  on  the  axial 
line,  which  we  find  aty^.  This  will  be  the  positive  focal 
point,  or  the  focal  distance  of  the  lens.  Also,  if  rays  of 
light  should  diverge  from  a  luminous  point  at  fp, 
they  would  pass  through  the  prism  in  the  same  lines  and 
emerge  parallel. 

You  will  note  that  the  angle  of  refraction  of  any  prism 


REFRACTION. 


Is  always  the  same,  no  matter  in  which  direction  the  rays 
of  light  may  pass.  This  same  explanation  holds  good  in 
the  case  of  a  bi-convex  lens,  whose  curved  surfaces  are 
simple  minute  planes  of  a  number  of  prisms  with  their 
bases  together. 

Now  if  the  surfaces  of  a  lens  are  perfectly  round,  being 
sections  of  a  perfect  sphere,  it  is  called  a  spherical  bi- 
convex lens  ;  and  the  ray  of  light  that  passes  directly 
through  the  centre,  in  line  with  the  perpendicular,  is  not 
refracted,  and  is  called  the  axial  ray  of  the  lens. 


Fi<;.  17. — A  BI-CONVEX     LENS  AND  ITS  POSITIVE  FOCAL  POINT. 

In  a  bi-convex  lens  the  parallel  rays  from  infinity, 
coming  from  a  direction  P,  will  fall  upon  the  convex  sur- 
face of  the  lens  C,  and,  passing  through,  will  be  bent  by 
the  lens  until  all  the  rays  will  meet  at  the  positive  focal 
point^,  and  then  passing  onward  will  diverge  ;  while  the 
axial  ray,  P  to  a,  passing  in  the  centre,  and  striking  the 
surface  of  the  lens  parallel  to  its  perpendicular  at  that 
point,  will  pass  onward  without  any  deviation. 

We  may  also  have  certain  rays  of  light  striking  the 
lens  on  other  portions  of  its  surface,  and  which  pass 
through  without  refraction,  as  all  those  rays  that  enter  the 
lens  parallel  to  the  perpendicular  at  the  point  of  entry 
are  not  refracted.  These  rays  are  called  the  secondary 
axes,  and  all  rays  passing  parallel  to  them  will  be  brought 
to  a  focal  point  on  each  secondary  axis. 

In  the  bi-convex  lens  C,  fig.  18,  with  parallel  rays  of  light 
passing  in  three  directions,  as  at  A,  B,  and  B ',  the  princi- 


28 


LECTURES  ON  THE  ERRORS  OF  REFRACTION. 


pal  axis  and  focus  are  found  on  the  line  A  to  A,  while  the 
secondary  axes  and  foci  are  shown  at  /?to  B,  and  B'  to  />". 
The  secondary  axes/? and  D'  strike  the  surface  coincident 
with  the  normal  at  that  point,  and  consequently  pass 
directly  through  the  lens,  while  all  other  rays  parallel  to 
these  axes  must  strike  the  lens  obliquely,  and  will  focus  at 
their  respective  secondary  focal  points  on  the  secondary 
axes,  as  shown  by  the  points^/" on  the  axes  B  and  />  , 
while  we  find  the  principal  focal  point  pf  on  the  principal 
axis  A  to  A. 


Fir..  18. — PRINCIPAL  AND  SECONDARY  Axis,  WITH  TIIKIR  FOCAL  POINTS. 

All  these  secondary  axes  must  pass  through  the  centre 
of  the  lens  at  the  nodal  point,  as  you  will  see  in  fig.  18, 
and  we  find  that  all  rays  of  light  that  coincide  with  the 
principal  or  secondary  axes  are  not  refracted,  but  that  all 
other  rays  parallel  to  these  axes,  when  passing  through  a 
bi-convex  spherical  lens,  are  brought  to  a  focus  at  the 
centre  of  curvature  of  its  curved  surfaces.  These  focal 
points  always  rest  on  the  principal  or  secondary  axes,  the 
first  being  the  principal  focal  point,  and  its  distance  from 
the  optical  centre  of  the  lens  represents  the  principal  focal 
distance,  or  the  refractive  power.  When  we  have  refer- 
ence to  a  lens  of  any  kind,  and  speak  of  the  focal  distance, 


REFRACTION.  2g 

you  will  understand  that  a  1 2-inch  lens,  for  instance,  has  its 
focal  point  at  twelve  inches  from  the  optical  centre.  Now 
each  lens,  either  positive  or  negative,  has  practically  two 
nodal  points,  situated  on  the  axis,  and  called  the  anterior 
and  posterior.  These  two  points  coincide  with  the  two 
principal  points,  situated  on  the  principal  axis,  at  the  optical 
centre  of  the  convex  surfaces.  Hence  all  the  rays  of  light 
that  strike  the  surfaces  of  the  lens  directed  toward  a 
nodal  point  will  pass  through  the  optical  centre  of  the 
lens,  and  emerge  as  if  they  came  from  the  other  nodal 
point,  in  a  direction  parallel  to  that  of  the  incident  ray. 

LANDOLT  tells  us  that  in  a  lens  surrounded  by  a  single 
medium,  as  the  air,  the  radius  of  the  first  surface  is 
to  that  of  the  second,  as  the  second  focal  distance  of  the 
first  is  to  the  first  focal  distance  of  the  second  ;  that,  in 
order  to  find  the  optical  centre  of  a  bi-convex  lens,  the 
thickness  of  the  lens  must  be  divided  into  two  parts, 
which  will  be  to  each  other  as  the  radii  of  the  corresponding 
surfaces.  Such  being  the  case,  the  optical  centre  will  be 
in  the  centre  of  the  lens  when  the  curved  surfaces  are 
equal,  and  nearer  the  more  convex  surface  when  they  are 
different  ;  and  further,  "  every  incident  ray  refracted  by 
the  first  surface  in  such  a  way  as  to  pass  through  the  opti- 
cal centre,  emerges  from  the  system  in  a  direction  parallel 
to  its  primitive  one." 

Let  us  illustrate  this  by  the  following  diagram,  fig.  19. 
On  the  principal  axis  we  have  the  two  curved  surfaces, 
one  more  convex  than  the  other,  representing  a  sec- 
tion of  a  bi-convex  lens.  Let  us  draw  through  the  cen- 
tre of  curvature,  C'  and  C",  of  the  two  surfaces  of  the 
lens  two  parallel  rays,  C' J'  and  C"J".  The  planes  tan- 
gent to  the  refractive  surfaces  at  J'  and  J"  are  parallel, 
since  they  are  perpendicular  to  the  parallel  rays  C'J'  and 
C"J".  Hence  if  the  ray  TJ'  meet  the  first  surface  at 
such  an  angle  that  it  follows  J'J"  in  entering,  the  cor- 


3O  LECTURES   ON  THE    ERRORS   OF  REFRACTION. 

responding  emergent  ray,  J"U,  will  be  parallel  to  the 
incident  ray,  for  the  ray  will  thus  have  passed  through  a 
refractive  medium  limited  by  parallel  surfaces,  and  the 
point  O,  where  the  r&yJ'J"  crosses  the  principal  axis,  will 
be  the  optical  centre  of  the  lens.  Then,  if  these  two  rays, 
the  incident  and  emergent,  be  prolonged  backward  in  a 
straight  line  to  the  principal  axis  of  the  lens,  we  will  have 
the  two  nodal  points.  When  these  lines  cross  the  axis,  as 


FIG.  19. — THE  OPTICAL  CENTRE,  ETC. — AFTER  LANDOLT. 

shown  by  the  points  K'  and  K' ',  so  that  the  incident  ray 
is  directed  toward  the  first  nodal  point,  while  the  emer- 
gent ray  takes  a  direction  as  though  coming  from  the 
second  nodal  point,  we  find  the  same  parallel  direction 
of  the  rays  when  coming  from  the  points  B  to  B'  and 
D  to  D't  but  each  ray  passes  through  the  optical  centre, 
O,  of  the  lens,  and  its  direction  is  either  toward  or  from 
the  two  nodal  points. 

But  we  must  remember  that  the  two  nodal  points  and 
the  optical  centre  of  the  lens,  as  illustrated  above,  refer  to 


REFRACTION.  31 

the  path  of  the  rays  through  thick  lenses,  while  in  thin 
lenses,  when  the  curved  surfaces  are  so  near  each  other, 
we  may  simply  conclude  that  our  secondary  axes  pass 
directly  through  the  optical  centre  of  the  lens  (see  fig. 
1 8),  and  that  all  rays  that  are  refracted  by  the  curved 
surfaces  will  have  the  same  direction,  as  they  pass  through 
the  lens,  when  coming  from  different  points  of  the  principal 
axis. 

If  you  will  now  notice  the  lens  D,  in  fig.  14,  you  will 
find  that  it  also  represents  two  prisms,  but  with  their 
apices  together  and  bases  outward.  Now  if  we  apply 
the  same  rules  of  refraction,  as  with  the  convex  lens,  to 
these  curved  surfaces,  we  will  find  that  as  the  parallel  rays 
of  light  emerge  from  the  lens  they  are  divergent,  being 
bent  toward  the  bases  of  the  prisms.  If  the  lens  surface 
be  spherical,  we  have  a  bi-concave  spherical  lens.  This 
lens  will  so  bend  rays  of  light  that  they  will  diverge  in  all 
directions,  as  if  they  came  from  some  point  behind  the 
lens.  It  is  consequently  called  a  negative  lens.  We  find 
the  focal  point  of  this  lens  situated  on  the  principal  axis, 
at  that  point  where  the  divergent  rays,  if  they  were  con- 
tinued directly  backward,  would  meet.  The  distance  of 
this  point  from  the  optical  centre  of  the  lens  is  called  the 
negative  focal  distance,  which  may  be  represented  by 
inches  or  dioptrics.  If  we  represent  this  distance  in 
inches,  then  a  bi-concave  spherical  lens  of  twelve  inches 
focal  distance  will  cause  parallel  rays  of  light  to  diverge, 
after  they  have  passed  the  lens  and  have  been  refracted, 
as  if  they  came  from  a  point  twelve  inches  behind  the 
lens,  on  the  principal  axis. 

In  this  diagram,  fig.  20,  we  represent  a  bi-concave  lens 
at  C,  with  the  parallel  rays  from  P,  which,  passing  through 
the  lens  and  being  bent  toward  the  bases,  are  divergent, 
as  at  A,  with  a  direction  as  if  they  came  from  the  negative 
focal  point  B,  as  shown  by  the  dotted  lines.  Thus  when 


ON  THE   ERKOKS   OF  KE1-KACTION. 


the  parallel  rays  strike  these  curved  surfaces  they  are  bent 
in  the  same  manner  as  when  they  strike  the  surface  of 
a  bi-convex  lens,  but  the  curvature  is  different,  as  the 
bases  are  now  outward  ;  therefore  the  direction  of  the 
rays  is  divergent  as  they  pass  through  the  lens. 


FIG.  20. — A  BI-CONCAVE  LENS,  WITH  ITS  NEGATIVE  FOCAL  POINT. 

The  remaining  lenses  in  fig.  14  all  refract  light  on  the 
same  principle  and  in  the  same  manner,  according  to  the 
curved  surfaces  that  are  presented  to  the  rays  of  light ;  those 
that  are  convex  bringing  the  rays  to  a  positive  focus,  and 
those  that  are  concave  causing  the  rays  of  light  to  diverge 
as  if  they  came  from  the  negative  focal  point,  /.  e.t 
behind  the  lens.  But  I  wish  to  call  your  attention  to  the 
lenses  marked  F  and  G.  These  are  called  meniscus  lenses. 
The  first  one,  F,  has  a  negative  and  a  positive  curved  sur- 
face, but  the  curvature  of  the  positive  surface  being  so 
much  greater  than  that  of  the  negative  surface,  the  rays 
of  light,  after  they  pass  through  the  lens,  are  brought  to 
a  positive  focal  point ;  while  in  the  lens  G,  called  ^concavo- 
convex,  the  negative  surface  has  the  greatest  refractive 
power,  and  now  the  rays,  as  they  pass  through  the  lens, 
diverge  from  the  negative  focal  point. 

Let  me  illustrate  this  to  you  by  a  reference  to  the  men- 
iscus lens  F,  in  which  we  will  suppose  that  the  curvature 
of  the  negative  or  concave  side  of  the  lens  is  equal  to  a  bi- 


REFRACTION. 


33 


concave  lens  of  -^,  and  that  the  curvature  of  the  positive  or 
convex  side  of  the  lens  is  equal  to  a  bi-convex  lens  of  -fa : 
thus  the  positive  focal  power  of  this  meniscus  lens  will  be 
equal  to  (-f  fa)  -  -  ( —  fa)  =  +  -fa.  The  power  of  the 
convex  surface  is  neutralized  by  the  concave  surface,  ac- 
cording to  their  respective  curvatures,  or  their  refractive 
power.  You  will  find  that  most  of  the  lenses  in  the  spec- 
tacles and  eye-glasses  of  the  shops,  particularly  those  of 
low  power,  are  ground  according  to  the  above  method. 

The  particular  advantage  about  these  meniscus  lenses 
is,  that  they  give  us  much  more  correct  secondary  axes, 
and  when  adjusted  to  the  eye  yield  more  perfect  vision 
through  the  periphery  of  the  glass,  rendering  the  field 
of  vision  much  larger  and  more  distinct. 

I  wish  you  to  remember  that  the  angle  of  refraction  is 
always  the  same  when  passing  through  a  concave  or  a  con- 
vex lens.  You  will  note  that,  when  the  luminous  point  is 
at  the  focal  distance  of  a  convex  lens,  the  emergent  rays 
are  parallel,  but  if  we  move  the  luminous  point  farther 
back  from  the  lens,  we  now  find  that  the  emergent  rays 
are  convergent  ;  while,  if  we  move  the  luminous  point 
nearer  to  the  lens  than  the  focal  distance,  the  emergent 
rays  become  divergent,  as  you  will  see  by  this  diagram  : 


TIG.  2i.— DIAGRAM  SHOWING  THE  ANGLE  OF  REFRACTION  IN  A  BI-CONVEX  LENS. 

In  the  above  figure  we  represent  a  bi-convex  lens  atZ> 
and  the  focal  point  at  A.     Now,  rays  from  that  point  will 


34       LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

pass  beyond  the  lens  in  parallel  lines,  a,  a,  a,  a,  but  if 
we  move  the  luminous  point  back  to  B,  we  find  that 
the  emergent  rays  are  convergent,  with  the  same  angle  of 
refraction,  and  if  continued  would  meet  at  b.  Then  if  we 
carry  the  luminous  point  nearer  the  lens,  inside  the  focal 
point  to  C,  the  emergent  rays  pass  beyond  the  lens  in  a 
divergent  direction  toward  c,  c,  c,  c,  with  the  angle  of  re- 
fraction the  same  as  when  the  rays  proceeded  from  the 
principal  focal  point.  We  have  the  same  result  with  the 
concave  lens,  but  when  the  luminous  point  is  nearer  the 
lens  than  its  focal  point,  the  emergent  rays  are  more  di- 
vergent than  the  refractive  power  of  the  lens,  and  they 
cannot  be  made  convergent. 

This  fact  of  the  angle  of  refraction  being  always  the 
same  is  beautifully  illustrated  in  the  human  eye,  as  I  shall 
show  you  when  we  study  the  refraction  of  the  dioptric  me- 
dia, which,  taken  collectively,  would  be  represented  by  a 
bi-convex  lens  of  the  same  focal  power. 

When  a  ray  of  light  parallel  to  the  visual  axis  strikes 
the  cornea  and  passes  through,  it  is  first  refracted  by  the 
outer  surface  according  to  the  rules  of  refraction.  The 
index  of  refraction  of  the  cornea  is  about  1.390,  and  the 
radius  of  curvature  0.28  to  0.32  inches.  The  rays  then 
pass  onward  as  shown  in  the  diagram,  fig.  n,  page  14. 
Through  the  aqueous  humor — whose  index  of  refraction 
is  equal  to  1.336,  they  now  pass  through  the  crystalline 
lens  and  its  capsule,  with  a  mean  refraction  of  1.3839, 
and  finally  through  the  vitreous  humor,  with  an  index  of 
refraction  of  1.339,  anc^  a^  tne  entering  rays,  by  the 
refraction  of  these  various  media,  are  brought  to  a  focus 
upon  the  retina,  on  the  fovea  centralis  at  the  yellow  spot. 

You  will  see  by  this  that  the  indices  of  refraction  of 
these  different  media  forming  the  dioptric  system,  through 
which  the  rays  of  light  pass,  are  nearly  all  the  same  ;  con- 
sequently the  principal  bending  or  refraction  of  the  rays 


REFRACTION.  35 

of  light  will  take  place  at  the  outer  surface  of  the  cornea, 
as  at  that  convex  spherical  surface  the  rays  pass  from  a 
light  medium,  the  air,  to  a  denser  medium,  the  dioptric 
media,  and  focus  upon  the  retina  at  the  macula  lutea,  in 
the  emmetropic  or  normal  eye,  the  ciliary  muscle  being  in 
a  state  of  complete  relaxation. 

As  these  rays  pass  through  the  dioptric  media,  I  wish 
to  call  your  attention  to  the  iris,  which  lies  between  the 
anterior  and  posterior  chambers  of  the  eye,  with  the  cor- 
nea in  front,  and  the  anterior  capsule  of  the  lens  behind. 
This  is  an  annular  opaque  diaphragm  shown  by  the  col- 
ored part  of  the  eye,  with  an  aperture  in  the  centre  called 
the  pupil.  This  opening  is  a  little  downward  and  to  the 
inner  side  of  the  optic  axis,  this  pupillary  space  in  man 
being  always  circular.  We  find  that  the  iris  has  two  sets 
of  muscular  fibres,  connective  tissue,  and  pigment.  The 
muscular  fibres  are,  first,  the  circular,  which  receive  their 
nervous  supply  from  the  third  nerve,  or  motor  oculi  com- 
munis,  by  a  filament  which  comes  through  the  ophthalmic 
ganglion,  and  the  radiate  fibres,  which  are  controlled  by 
the  sympathetic  system  of  nerves,  these  radiate  fibres  be- 
ing antagonistic  to  the  circular  ones. 

The  object  of  the  iris  is  very  similar  to  that  of  an  or- 
dinary diaphragm  in  an  optical  instrument.  As  the  nervous 
system  is  stimulated  by  the  illumination  and  light  that 
passes  in  the  eye  as  well  as  in  the  act  of  accommodation, 
so  the  iris  regulates  the  amount  of  light  passing  to  the 
retina.  In  a  bright  light  the  iris  is  contracted  and  the 
pupil  very  small,  while  at  night,  in  a  subdued  light,  the 
iris  is  dilated  and  the  pupil  large.  The  iris  also  serves  to 
correct  the  spherical  aberration  of  the  cornea  or  lens,  as 
by  its  contraction  it  will,  cut  off  all  the  peripheral  rays  that 
pass  through  the  margins. 

For  the  purpose  of  correcting  errors  of  refraction  in  the 
eye,  and  found  in  all  the  cases  of  trial  glasses,  we  have  sets 


36  LECTURES  ON  THE  ERRORS  Of  REFRACTION. 

of  lenses  whose  action  is  quite  different  from  that  of  those 
hitherto  described.  These  are  called  cylindrical  lenses,  as 
they  are  practically  segments  of  a  cylinder  with  the  a. vis 
of  the  cylinder  at  right  angles  to  the  refracting  surface  ; 
they  are  generally  plane  on  one  side,  with  the  refracting 
surface  on  the  other,  and  may  be  either  concave  or  con- 
vex. You  will  remember  the  lenses  I  have  spoken  about 
are  all  perfectly  spherical,  with  their  refractive  power  ex- 
actly the  same  in  all  meridians,  so  that  the  rays  are  either 
brought  to  a  positive  focus,  or  diverged  as  from  a  nega- 
tive focus. 

Now  if  we  study  the  action  of  the  cylindrical  lens,  we 
must  consider  chiefly  all  the  rays  as  passing  in  two  princi- 
pal planes  at  right  angles  to  each  other.  While  the  light 
also  passes  in  any  number  of  intermediate  planes,  yet  the 
rays  are  so  bent  that  in  the  convex  cylindrix  lens  they 
will  focus  at  a  positive  point,  there  simply  forming  a  line, 
and  not  a  single  point,  as  in  a  spherical  lens. 

The  two  principal  planes  of  the  eye  are  generally  verti- 
cal and  horizontal,  with  the  intermediate  planes  (let  me 
here  refer  you  to  the  Lectures  on  Astigmatism);  but  you 
must  remember  that  these  principal  planes  will  always  be 
at  right  angles  to  each  other,  and  may  be  at  any  degree 
of  the  arc  of  a  circle,  as  I  have  illustrated  by  this 
diagram  : 


FIG.  22. — THE  POSITIONS  OF  THE  MERIDIANS  OR  PLANES. 


REFRACTION. 


37 


The  vertical  and  horizontal  planes  are  shown  by  the 
lines  A,  B,  but  instead  of  that  position  o.ne  principal  plane 
may  be  at  C,  or  45°,  and  the  other  will  then  be  at  D,  or 
135°,  or  these  two  principal  planes  may  be  at  any  of  the 
meridians  on  the  arc  of  a  circle.  Then  if  we  make  a  glass 
whose  refractive  power  will  be  only  on  the  rays  of  light 
of  one  meridian,  the  rays  that  pass  in  the  meridian  at  right 
angles  to  that  will  pass  parallel,  and  are  not  refracted.  . 

Now,  a  cylindrical  lens  is  one  that  is  a  section  of  a  cyl- 
inder ;  for  if  we  take  a  cylinder  of  glass,  with  the  axis 
running  directly  through  its  centre,  and  cut  off  a  section 
parallel  to  its  axis,  the  rays  of  light  that  pass  through  in  a 
plane  that  is  the  same  as  the  axis  will  not  be  refracted  ; 
but  all  those  passing  at  right  angles  to  that  plane  will  be 
either  convergent  or  divergent,  according  to  the  refract- 
ing power  of  the  glass  and  the  radius  of  curvature. 


FIG.  23. — END  OF  CYLINDER,  FROM  WHICH  THE  CYLINDRIC  GLASS  is  CUT. 

In  this  diagram  we  have  the  end  of  the  cylinder  of  glass, 
with  its  axis  at  a.  If  we  make  a  section  at  B,  the  part 
cut  off  will  form  a  plano-convex-cylindric  lens  ;  a  section 
made  through  this  at  C  will  present  the  surface  of  a  rect- 
angle, and  all  the  rays  in  that  plane  will  strike  the  glass 
parallel  to  its  perpendicular  and  will  not  be  refracted. 

The  action  of  a  plano-convex-cylindric  lens  is  shown  in 
the  diagram  on  p.  38,  in  which  A  shows  the  action  of  par- 
allel rays  of  light  in  a  plane  at  right  angles  to  the  axis  of 
the  glass  ;  and  B,  the  parallel  rays  in  a  plane  coincident 
to  the  axis.  Hence  we  have  this  rule  :  that  the  cylindric 


38       LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

lens  will  only  converge  or  diverge  all  rays  of  light  that 
pass  at  right  angles  to  its  axis,  according  to  the  refractive 
power ;  consequently   the    refracted   rays   of  a    cylindric 
glass  are  never  brought  to  a  focal  point,  but  will  form  a 
straight  line  on  a  screen  placed  at  its  focal  distance. 

In  the  complete  cases  of  trial  glasses  as  found  in  the 
shops,  we  have  thirty-two  pairs  of  each,  convex  and  con- 
cave spherical  glasses,  either  with  ground  edges  or  set  in 
frames  with  handles ;  also  nineteen  pairs  of  each,  convex 
and  concave  cylindric  glasses,  with  the  axis  of  each  glass 
marked  by  a  small  line  at  the  edge. 


FIG.  24. — PLANES  OF  LIGHT  WITH  REFRACTION,  IN  THE  TWO  PRINCIPAL  MERIDI- 
ANS OF  A  CYLINDRIC  LENS.  B,  THE  AXIAL  PLANE. 

There  is  also  a  metal  disc,  for  covering  the  eye  ;  a 
stenopaic  slit,  for  testing  the  meridian,  the  opening  be- 
ing adjustable  ;  a  set  of  prisms  with  a  principal  angle  of 
from  2°  to  20° ;  sets  of  colored  glasses,  different  shades  of 
red  and  blue  ;  and  a  trial  frame,  in  which  any  of  the 
glasses  may  be  placed — the  whole  in  a  neat  rosewood  or 
leather  case.  With  these  trial  cases  you  can  test  all  vari- 
eties of  refraction. 

This  completes  the  description  of  the  action  of  the  vari- 


REFRACTION.  39 

cms  lenses  found  in  the  cases  of  trial  glasses.  Let  us  now 
study  the  method  of  using  these  glasses  for  the  correction 
of  the  errors  of  refraction  as  found  in  the  human  eye.  I 
shall  give  you  illustrative  cases  that  may  require  any  of 
the  spherical  lenses,  separate  or  combined,  for  the  correc- 
tion of  refraction  and  the  relief  of  asthenopia. 

I  have  used  the  word  inches  in  designating  the  focal 
distance  of  the  lenses.  But,  at  the  present  time,  there  is  a 
strong  tendency  among  all  ophthalmologists  to  use  the 
French  metric  system  to  designate  the  focal  strength  of 
a  lens.  You  should  therefore  familiarize  yourselves  with 
that  system,  as  compared  with  the  old  method  of  notation. 

The  old  method  was  somewhat  unsatisfactory,  on  ac- 
count of  the  difficulty  of  adding  or  subtracting  the  vari- 
ous fractions  in  compound  lenses,  and  also  in  the  varying 
size  of  the  inch  of  different  countries,  as  follows  : 

The  Paris  inch,         —  27.07  millimetres. 

The  English  inch,    =  25.3 

The  Austrian  inch,  =  26.34 

The  Prussian  inch,  =  26.15 

You  will  note  that  there  is  a  wide  disproportion  in 
this  measure,  a  lens  of  5  inches  [English]  being  quite 
different  from  one  of  5  inches  [Paris]  in  its  focal 
distance  ;  also,  that  the  standard,  one  inch,  of  the  old 
system  is  so  strong  that  we  seldom,  if  ever,  use  it.  Now, 
according  to  the  old  system,  where  the  standard  i  =  one 
inch,  a  lens  of  two  inches  focal  distance  will  be  only  one 
half  as  strong,  =  ^,  all  the  weaker  lenses  in  proportion 
being  represented  by  smaller  fractions,  as  a  ten-inch 
lens  =  j\,  a  twenty-inch  lens  =  ^-,  and  so  on.  Thus  a 
glance  will  show  how  tedious,  not  to  say  difficult,  it  is  to 
add  to,  or  subtract  from,  those  fractions. 

The  new  or  metric  system,  which  was  adopted  by  the 
Ophthalmological  Society,  which  convened  at  Heidelberg 
in  1875,  takes  as  its  unit  of  measure,  a  dioptry  [D]  as  pro- 


40  LECTURES  ON  THE  ERROKS  O/-    REFRACTION. 

posed  by  Monoyer,  and  has  one  metre  as  its  standard  focal 
distance,  represented  by  ^,  then  No.  2  =  -"'-,  or  2  D, 
and  No.  4  LJi,  or  4  D.  This  glass  of  4  D  is  four  times  as 
strong  as  the  standard  of  i  D,  the  unit  of  measure,  its 
focal  distance  being  equal  to  one  fourth  of  a  metre. 

This  system  gives  us  a  series  of  lenses,  of  one  dioptry 
between  each  glass,  but  as  it  has  been  found  that  for  prac- 
tical use  other  lenses  are  needed,  we  use  the  fractions 
of  a  dioptry  to  make  the  regular  series,  weaker  or 
stronger.  Thus,  for  instance,  should  we  need  a  lens  be- 
tween i  D  and  2  D,  we  can  add  a  .5  D  to  a  i  D,  and  we 
have  a  lens  of  1.50  D,  equal  to  about  24  inches  ;  or,  should 
we  need  a  lens  weaker  than  that  of  i  D,  we  may  divide 
it,  and  have  a  lens  of  J  or  0.75  D,  \  or  0.50  D,  and  \  or 
0.25  D. 

To  give  you  a  more  correct  understanding  of  the  rela- 
tive value  of  the  old  and  the  new  system,  the  following 
table  will  show  the  focal  distance  of  the  lenses  in  general 
use.  If  we  take  the  metre  as  our  standard  and  consider 
it  equal  to  about  40  inches  (though  the  metre  is  exactly 
equal  to  39.5  Paris  inches,  but  for  practical  purposes  we 
may  calculate  it  as  40  inches),  then  we  can  readily  find 
the  focal  distance  of  a  lens,  in  inches,  by  dividing  40  by 
the  number  of  the  dioptry  ;  or  we  can  find  the  number  of 
the  dioptry  by  dividing  40  by  the  number  of  inches. 

According  to  the  above  method  of  calculation,  the  focal 
distance  of  a  lens  is  the  inverse  of  its  refractive  power. 
Thus  a  lens  of  5  D  will  equal  40  divided  by  5,  equal  to  8 
inches,  etc.  ;  or  as  a  lens  is  the  inverse  of  its  refractive 
power,  then  the  lens  of  5  D,  ^-p  or  l~-\  will  give  a  focal  dis- 
tance of  20  cm.,  or  about  8  inches.  In  the  same  way  we 
can  find  the  number  of  the  dioptry,  which  is  the  inverse 
of  the  focal  distance.  As,  for  example,  if  a  lens  of  10 
inches  focal  distance  be  equal  to  25  cm.,  then  we  have  4r» 

loo  cm.        T~\ 

-—  —  4  \J. 


REFRACTION. 


•COMPARATIVE    LIST    OF    THE    METRIC    AND    INCH    SYSTEM. 


Dioptrics,  or  new  system. 

Approximate    value    in 
inches. 

Actual  value  in  inches. 

O  25 

160 

.    157.4740 

0.50 

...         80       ... 

78.717O 

0.75     .     .     . 
I 

...        53       ... 
40 

.    .    .    52.4931 

IQ  1685 

I.fl* 

12 

^1.4048 

I    5O 

...           26        ... 

26  2456 

1.75     .     .     . 

2 

.      .      .           22         ... 
2O        . 

.     .     .     22.4963 
19  6842 

2  25 

...        18       .     .     . 

17  4071 

2   5O 

...        16       .     .     . 

I5.747d 

2  75 

14 

I4.1IO6 

r« 

...       13  1228 

•3    25 

12         ... 

12   I  I  30 

1  5O 

II         ... 

.        II.248I 

4 

.  '  .                 IO        ... 

9.8421 

4  50 

q 

8.7485 

5. 

...          8       ... 

.       .          7.8737 

e   SQ 

7       ... 

7.I57Q 

6          ... 

64     , 

6.  ^614 

6.  50 

...          6       ... 

6.0567 

7.         ... 

5i     • 

5.6240 

8.         ... 

.     .     .          5      ... 

4.Q2IO 

4i     . 

4-3743 

10. 

1.0168 

11.         ... 

l£     . 

1.5780 

12. 

ll     . 

1.2807 

n. 

^ 

3.0283 

14. 

2f      . 

2  8l2O 

16 

2j 

2  46O5 

18 

24-      . 

.       .       .          2.I87I 

20 

2         ... 

1.9684 

You  will  see  by  the  above  tables,  or  by  the  simple 
rules  of  changing  the  calculations,  taking  40  (39.5) 
inches  as  the  length  of  the  metre,  that  you  can  readily 
tell  the  focal  distance  of  a  lens,  marked  in  dioptrics  or 
inches  :  as  in  one  case  you  simply  divide  40  by  the  num- 
ber of  dioptrics,  which  gives  you  the  number  of  inches  ; 
or  you  divide  40  by  the  refracting  power  in  inches, — this 
giving  you  the  number  of  the  dioptry. 

These  simple  rules  of  calculation  are  in  constant  use, 
not  only  in  estimating  the  power  of  a  lens,  marked  in 
dioptrics  or  inches,  but  many  of  our  best  ophthalmoscopes 
are  now  only  marked  in  dioptrics  ;  and  as  you  may  fre- 
quently wish  to  know  the  focal  power  in  inches,  you  can 
quickly  do  so  by  these  calculations. 


42  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

As  I  have  not  confined  myself  to  any  system  of  nota- 
tion in  this  work,  and  I  shall  use  the  inch  or  the  dioptric 
system  as  seems  most  suitable  at  the  time,  so  I  wish 
you  to  be  familiar  with  both  systems. 

In  completing  your  studies  on  refraction,  I  would  re- 
fer you  to  LANDOLT  on  "  The  Refraction  and  Accommoda- 
tion of  the  Eye  "  for  a  full  and  complete  explanation  of 
the  refraction  of  light  when  passing  through  different 
curved  surfaces.  These  lectures  are  mainly  intended  to 
aid  you  in  your  daily  clinical  work  in  correcting  the  errors 
of  refraction,  and,  above  all,  to  incite  you  to  earnest  study 
of  the  more  elaborate  works  on  this  most  interesting  sub- 
ject. 


THIRD  LECTURE. 

EMMETROPIA. 

Normal  refraction — Visual  acuteness — Conjugate  foci — Size  of  image — The  test 
types — Visual  angle — Infinity — Distance  of  testing — Vision  better  than  normal 
— Test  for  illiterate  persons — Method  of  recording — Field  of  vision — Perim- 
eters— Scotomata — Convergence  of  visual  lines — Glasses  prescribed. 

GENTLEMEN  : — As  I  propose  in  our  lectures  to  con- 
sider only  vision  and  the  errors  to  which  it  may  be 
subjected,  and  having  explained  the  various  anatomical 
parts  concerned  in  the  sense  of  sight,  also  the  action  of 
our  means  of  correction,  as  lenses,  etc.,  as  the  rays  of  light 
pass  into  the  eye  through  the  dioptric  apparatus,  we  will 
now  examine  the  normal  eye  in  its  power  to  see  and  ap- 
preciate the  objects  around  us. 

I  shall  speak  of  the  normal  eye  first,  though  I  believe 
that  there  are  very  few  persons  who  have  perfectly  normal 
vision  even  from  their  birth,  although  perhaps  many  of 
them  have  had  no  trouble  with  their  eyes,  and  have  al- 
ways supposed  their  sight  was  equal  to  that  of  the  perfect 
standard.  This  fact  was  well  demonstrated  a  few  years 
ago  by  Prof.  D.  B.  St.  John  Roosa,  in  an  examination  of 
a  number  of  gentlemen,  all  students,  whose  ages  ranged 
from  twenty-one  to  thirty-two  years,  who  had  never  been 
conscious  of  any  visual  weakness,  and  whose  eyes  were 
examined  under  the  influence  of  atropia,  the  accommoda- 
tion being  completely  at  rest.  The  results  of  this  exami- 
nation were,  that  only  one  fifth,  or  about  20  per  cent,  had 
normal  eyes. 

43 


44  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

My  friend,  the  late  Dr.  Edward  T.  Ely,  also  examined 
one  hundred  cases  of  infants'  eyes,  with  the  ophthalmo- 
scope, and  found  a  very  small  number  with  normal  eyes  ; 
nearly  all  of  them  having  the  short  eyeball.  I  should  think 
from  this  that  ametropic  eyes,  or  eyes  that  are  not  normal, 
in  reference  to  their  refraction,  and  do  not  focus  rays  of 
light  upon  the  retina  when  at  rest,  exist  in  the  largest 
number ;  though  they  may  not  suffer  from  any  of  the 
symptoms  of  asthenopia,  or  weak  sight. 

By  the  normal  eye,  I  mean  one  that  when  in  a  state  of 
rest  has  its  refractive  power  so  adjusted  that  it  can  see 
distinctly,  at  a  remote  point  or  infinity  ;  so  that  parallel 
rays  of  light  are  brought  to  an  exact  focus  on  the  retina, 
at  the  macula  lutea.  This  is  called  the  emmetropic  < 
Landolt  says:  "The  emmetropic  eye  is  one  the  retina  of 
which  is  found  at  the  principal  focus  of  its  dioptric  system, 
or  one  which  unites  parallel  rays  on  its  retina,  or,  ex- 
pressed in  another  manner,  the  punctum  remotum  of 
which  is  situated  at  infinity."  To  this  I  might  add,  that 
an  emmetropic  eye  is  one  whose  refractive  power  is  such 
that  rays  passing  from  the  retina  through  the  dioptric 
media  pass  outward  in  parallel  lines. 

Let  us  test  an  emmetropic  eye,  and  what  will  be  the 
results  of  the  examination,  as  regards  the  vision  at  a  dis- 
tance and  at  the  near  point  ?  Suppose  the  V  =  |^,  and  the 
nearest  point  of  distinct  vision  for  the  smallest  type  five 
inches,  the  person  examined  being  twenty  years  of  age  ; 
in  such  a  case  the  visual  acuteness  =  i,  as  the  person  has 
distinct  vision  at  infinity  with  the  eye  at  rest.  By  visual 
acuteness,  I  mean  that  power  of  the  nervous  elements  of 
the  eyeball  (the  retina)  to  see  and  appreciate  certain 
objects,  as  test-letters,  at  a  specified  distance,  whose 
standard  is  |$  =  i . 

You  are  probably  aware  that  when  rays  of  light  from 
an  object  pass  through  the  dioptric  media  they  will  be 


EMMETROPIA. 


45 


brought  to  an  exact  focus  on  the  retina,  and  there  form  a 
distinct  inverted  image. 

We  know  that  there  is  an  inverted  image  formed  at  the 
focal  point  of  the  dioptric  system,  as  the  entire  refractive 
apparatus  has  the  same  effect  on  the  rays  of  light,  either 
parallel  or  divergent,  as  a  simple  convex  lens.  Now  the 
image  formed  by  a  convex  lens  is  according  to  the  laws  of 
the  conjugate  foci,  which  I  will  explain  to  you  in  this 
manner  :  If  we  pass  the  divergent  rays  from  a  luminous 
point  through  a  bi-convex  lens,  they  will  be  refracted  and 
brought  back  to  a  point,  at  the  focal  distance  of  the  lens. 
You  can  readily  prove  this,  and  should  do  so,  by  using  for 
your  luminous  point  a  very  small  flame  ;  you  must  also 
have  a  screen  to  receive  the  rays  after  they  have  passed 
through  the  lens,  and  when  in  their  proper  positions  the 
rays  from  the  flame  will  focus  on  the  screen.  We  can 
reverse  the  direction  of  the  rays  by  placing  the  luminous 
point  in  the  position  of  the  screen,  and  the  screen  where 
the  flame  was,  and  we  find  the  same  focal  point  of  the  lens. 
From  this  experiment  we  have  two  focal  points,  a  first  or 
anterior,  and  a  second  or  posterior,  and  these  two  points 
are  the  conjugate  foci  of  each  other. 

You  must  remember  that  when  the  rays  from  any  il- 
luminated object  pass  through  a  bi-convex  lens  each  point 
on  its  surface  sends  off  divergent  rays,  which  by  the  ac- 
tion of  a  lens  are  again  brought  to  a  point.  This  point  is 
on  the  axial  ray,  which,  proceeding  from  a  point,  strikes 
the  surface  of  the  lens  coincident  with  the  normal,  and  is 
not  refracted. 


FIG.  25. — THE  CONJUGATE   Foci  OF  A  BI-CONVEX   LENS.     THE  DOTTED    LINES 

SIMPLY  SHOW    THE    COURSE    OF    RAYS    IN    OTHER    PARTS    OF    THE    LENS. 


46       LECTURES  ON  THE  ERRORS  OF  REFRACT/OX. 

Now  take  .the  course  of  the  rays  as  they  proceed  from? 
the  three  points,  A,  B,  and  C,  on  the  large  arrow,  with 
the  principal  axis,  /",  and  secondary  axes,  e,  g.  These  are 
the  rays  from  each  point  that  strike  the  lens  perpendicu- 
lar to  its  surface,  and  are  not  refracted.  We  also  find 
that  all  other  rays,  as  they  strike  the  lens  on  all  parts  of  its 
surface,  from  each  individual  point,  pass  through,  arc  re- 
fracted, and  brought  back  to  an  exact  focus  upon  the  same 
axis  from  which  they  started.  All  the  rays  from  A  will 
focus  at  A',  also  from  B  at  B',  and  from  C  at  C,  with  each 
axial  ray  passing  through  the  nodal  point  D,  or  optical 
centre  of  the  lens. 

As  all  these  secondary  axes  must  cross  the  principal 
axis  at  the  nodal  point  of  the  lens,  you  will  readily  under- 
stand why  the  image  of  the  arrow  is  reversed  when  formed 
at  the  focal  point.  As  the  rays  are  refracted  the  image 
becomes  reversed,  and  very  much  diminished  in  size, 
according  to  the  distance  of  the  object  from  the  lens. 

Should  you  wish  to  estimate  the  size  of  this  retinal 
image  at  any  time,  I  will  give  you  a  simple  rule.  If  you 
have  the  size  of  the  object  and  its  distance  from  the  nodal 
point,  you  may  then  make  your  calculations  in  this  way  : 
The  size  of  the  object  added  to  the  distance  of  the  nodal 
point  from  the  retina,  which  you  will  remember  equals 
15.1501  mm.,  and  divided  by  the  distance  of  the  object 
from  the  eye,  plus  the  distance  of  the  nodal  point  from  the 
cornea,  which  equals  7.4969  mm.,  will  give  us  the  size  of 
the  retinal  image. 

You  can  more  readily  understand  how  to  estimate  the 
size  of  an  image  from  fig.  26,  which  not  only  illustrates 
the  conjugate  foci,  but  also  the  method  of  calculating  the 
size  of  the  retinal  image.  Our  formula  would  be  from 
this  diagram  :  ££J-J^  =  a'  b'.  We  would  have  the  same 
sized  image  if  a  smaller  object  were  placed  at  the  position  of 
x  or  y. 


EMMETROPIA. 


47 


We  will  not  discuss  the  question  why  the  image  being 
reversed  on  the  retina  does  not  appear  so  to  the  observer, 
as  the  subject  has  not  been  finally  settled,  and  I  believe 
never  will  be,  as  it  is  an  act  of  nature,  that  we  learn  from 
the  cradle.  When  the  sensitiveness  of  the  retina  is  estab- 
lished, when  the  infant's  eye  first  begins  to  notice  the  bright 
light  of  a  lamp,  then  the  brain  sees  it  inverted,  and  so 
it  appears  through  life. 


FIG.  26. — THE  CONJUGATE  Foci  OF  THE  EYE  AND  ESTIMATION  OF  THE  SIZE  OF 

RETINAL  IMAGE. 

Now  the  percipient  elements  of  the  retina  may  not  be 
developed,  perhaps  from  neglect,  congenital  causes,  or 
from  non-use,  and  then  it  will  require  a  much  larger 
image  to  convey  a  positive  impression  to  the  brain. 

If,  then,  we  consider  that  the  visual  acuteness  of  the 
retina  =  i,  on  what  will  this  fact  depend,  and  how  shall 
we  test  it  ? 

I  prefer  to  use  the  test-types  adopted  by  Snellen,  who 
has  selected*  such  letters  that  the  width  of  each  line  at  the 
proper  distance  from  the  eye  will  form  two  opposite  points 
on  the  retina.  These,  with  the  nodal  point,  subtend  an 
angle  of  one  minute  ;  the  black  lines  of  all  these  test-let- 
ters will  make  an  image  of  that  size  (one  minute)  in  its 
smallest  part.  Now  if  we  take  five  lines,  or  five  spaces, 
for  the  size  of  each  letter,  we  will  then  form  an  image 
upon  the  retina  which  subtends  an  angle  of  exactly  five 
minutes,  that  being,  in  a  majority  of  cases,  the  smallest 
visual  angle  and  image  that  the  normal  retina  can  ap- 
preciate. 


LECTURES  ON  THE  ERRORS  OF  AV-,/A'./(  77O.\  . 


To  fully  understand  this  visual  angle,  you  will  note 
that  if  we  take  the  two  most  opposite  points  of  a  test- 
letter,  which  should  be  distinctly  seen  at 
twenty  feet,  and  is  placed  at  that  distance 
from  the  eye,  rays  of  light  from  these  two 
points,  the  secondary  axes  of  their  conju- 
gate foci,  will  cross  at  the  optical  centre 
of  the  dioptric  system. 

This  is  shown  in  the  drawing  by  the 
lines  B  to  B'  and  C  to  C',  crossing  at  the 
nodal  point  a,  and  proceeding  to  the  re- 
tina. We  will  then  have  an  angle  aB '  C ', 
with  the  base  at  the  retina,  and  the  apex 
at  a,  the  nodal  point.  Now  the  angle,  as 
above,  that  can  usually  be  formed  by  a 
letter  is  one  of  5',  giving  an  angle  of  i', 
as  that  of  the  several  different  parts  of  the 
letter  and  its  intermediate  spaces,  this 
being  the  smallest  image  that  can  be  ap- 
preciated by  the  retina.  All  the  larger 
letters  on  the  test-cards  will  subtend  the 
same  angle  when  placed  at  their  respective 
distances,  as  the  largest  letter  when  placed 
at  200  feet  should  give  the  same  visual 
angle  as  the  smaller  letters  placed  at  a  dis- 
tance of  20  feet  from  the  eye  to  be  tested  ; 
it  is  also  very  obvious  that  we  have  the 
same  angle  with  the  other  letters  at  30, 
40,  or  50  feet.  Consequently  an  eye  that 
can  see  the  smaller  letters  at  20  feet  should 
also  see  the  larger  letters  at  30  feet,  or  the 
largest  letter  at  200  feet. 

Now  you  will  have  observed  that  I  use 
the  fraction  to  express  the  degree  of  visual  acuteness  whose 
numerator  represents  the  distance  at  which  the  letters  were 


EMMETROPIA.  49 

seen,  and  whose  denominator  represents  the  distance  at 
which  the  letters  should  be  read.  The  cards  of  test-types  now 
in  use  have  different  sizes  of  letters  that  should  be  read 
easily  at  certain  distances,  as  are  marked  on  each  card  ;  at 
the  same  time  you  will  have  also  seen  that  they  all  form 
an  image  on  the  retina  whose  angle  is  always  the  same, 
that  is,  an  angle  of  5! 

Thus  No.  20  should  be  read  distinctly  at  20  feet,  No. 
40  at  40  feet,  No.  rooat  100  feet,  and  so  on  ;  but,  if  we  take 
20  feet  as  the  standard  of  infinity,  and  if  at  that  distance  the 
observer  can  only  see  letters  that  should  be  seen  at  40  feet, 
V  will  then  equal  |~§-  according  to  our  rule  for  using  frac- 
tions, in  which  the  numerator  represents  the  distance  of 
the  test,  and  the  denominator  the  distance  at  which  the 
letters  should  be  seen  distinctly. 

Now  all  rays  that  come  from  20  feet  or  infinity  must 
be  practically  parallel ;  then  if  the  eye  is  emmetropic — i.  e.y 
adapted  for  these  rays — the  letters  which  should  be  seen  at 
20  feet  will  form  a  perfect  image  on  the  retina.  I  would 
advise  you  to  always  test  your  cases  at  20  feet,  as  it  is  the 
standard  distance,  while  I  think  we  get  better  results  in 
our  examination  of  the  vision. 

You  will  also  meet  with  some  cases  that  can  see  better 
than  !$.  Their  vision  is  above  the  normal  standard  and 
its  acuteness  is  equal  to  f-f ,  or  even  |£,  by  which  I  mean 
that  they  can  read  letters  at  20  feet  that  should  only  be 
read  at  15  or  10  feet;  therefore  their  vision  is  above 
or  better  than  the  standard. 

You  must  not  be  surprised  at  this,  as  you  will  find  it  the 
result  of  examination  of  the  eyes  of  many  young,  healthy 
persons  whose  dioptric  media  and  nervous  elements  are 
perfect.  But,  some  standard  must  be  adopted,  and  Snel- 
len's  test-letters  at  20  feet  is  about  the  greatest  distance 
for  normal  vision  in  the  largest  number  of  cases  :  from 
this  we  would  expect  in  all  our  examinations,  if  possible, 


50  LECTURES  ON  THE  ERRORS  O/-    REFRACTION. 

to  make  the  person  examined  at  least  see  |j|.  When  you 
wish  to  record  the  results  of  your  examination,  take  for  the 
acuteness  of  vision  V  =  the  numerator,  or  distance  at 
which  the  letters  are  seen,  =  d,  and  for  the  denominator 
the  distance  at  which  the  letters  ought  to  be  seen,  =  D.  We 
have  the  fraction,  5,  which  in  the  normal  or  emmetropic 
eye  would  be  V  =  |-&;  then,  if  not  up  to  this  standard, 
we  must  decide  that  the  visual  acuteness  is  below  normal, 
and  you  should  endeavor  to  correct  it  by  glasses  if  possi- 
ble. Among  our  patients,  particularly  at  the  clinics,  we 
meet  persons  with  diminished  sight  or  weakness  of  vision, 
but  so  illiterate  that  they  cannot  read  letters.  In  such 
cases  we  use  a  sign,  adopted  also  by  Snellen,  in  the  shape 
of  the  letter  E,  which  is  square,  with  one  side  open  and  the 
ends  pointing  in  different  directions,  as  upward,  down- 
ward, to  right  or  left,  as  Uj  fT|?  E,  3.  This  method  is 
of  service  also  with  children  and  mutes.  They  are  of  the 
same  size  as  the  ordinary  test-letters,  and  are  recorded  in 
the  same  way,  as  V  =  |^,  and  so  on. 

Snellen's  test-types  are  in  almost  universal  use,  and  I 
think  they  are  suited  for  all  practical  purposes.  At  the 
same  time  you  should  know  that  there  are  other  test-types 
in  use  in  different  countries  and  with  different  letters,  par- 
ticularly those  of  Green,  Dennett,  and  Monoyer ;  but  I  do 
not  think  they  have  any  practical  value  over  Snellen's. 

This  is  our  principal  test  for  the  acuteness  of  vision, 
and  it  is  not  only  very  simple  and  practical,  but  it  also  gives 
us  a  test  for  all  errors  of  refraction,  as  I  shall  show  you 
when  we  study  our  cases  of  ametropia. 

In  the  use  of  test-types  you  will  remember  that  the  illu- 
mination of  the  letter's  makes  a  great  difference.  It  should 
always  be  about  the  same,  with  a  good  clear  light  from  a 
window  and  the  observer  placed  so  that  the  light  will  not  be 
unpleasant  to  the  eye.  You  should  also  avoid  reducing  the 
fractions,  in  your  records  of  the  acuteness  of  vision  :  as, 


EMMETROPIA.  51 

for  instance,  if  V  =  f|f,  T57,  or  ^,  you  should  record  it  as 
|{j  only,  because  the  smaller  letters  may  not  be  seen  at 
the  shorter  distance,  as  those  for  10  feet  may  not  be  seen 
at  5  feet,  and  so  on.  Nor  does  it  give  us  a  true  record, 
while  that  of  |$  shows  exactly  the  distance  at  which  the 
person  was  tested  and  the  smallest  letters  that  could  be 
read  at  that  distance.  If  you  use  the  distance  of  16  feet 
for  your  test,  or  infinity,  then  the  numerator  will  be  in 
all  cases  16,  and  V  =  ^,  -L|,  etc. 

If  we  find  that  in  the  emmetropic  eye  V  =  |~[j-  or  less, 
we  should  examine  the  sensibility  of  the  retina,  not  only 
at  the  macula,  but  in  all  the  peripheral  parts.  Although 
in  these  eccentric  portions  V  does  not  equal  |-^,  still  we 
should  know  that  the  perceptive  elements  are  in  a  normal 
•condition,  and  that  the  sensibility  of  the  retina  is  not 
deficient  in  any  of  its  parts.  The  power  to  see  with  the 
peripheral  portions  may  be  diminished  by  some  patho- 
logical conditions,  as  in  glaucoma,  partial  detached 
retina,  etc. 

For  this  examination  the  most  simple  manner  of  test  is 
to  sit  in  front  of  the  person  to  be  examined,  and  as  you 
cover  one  eye,  direct  the  patient  to  look  at  your  own  eye, 
at  a  distance  of  about  two  feet  ;  then  keeping  the  optic 
axis  of  the  examined  eye  directly  forward,  you  will  hold 
the  hand  or  a  pencil  at  different  positions  around  and  in 
front  of  the  eye,  and  as  far  away  as  possible.  The 
farthest  point  at  which  the  finger  or  pencil  can  be  seen 
will  give  the  quantitative,  and  the  distance  at  which  the 
fingers  can  be  counted  will  give  the  qualitative,  field  of 
vision.  If  you  use  your  right  eye  at  the  same  time  you 
test  the  left  eye  of  your  patient,  and  hold  the  finger  or 
pencil  just  between  the  eyes,  you  can  compare  the  field  of 
your  eye  with  the  examined  eye. 

Another  good  method  is  to  place  the  person  to  be  ex- 
amined before  a  blackboard,  at  a  distance  of  about  twelve 


LECTURES   OAr  THE   EA'A'OKS   OF  A'/-:f'A'.H'77O.Y. 


inches,  and  with  one  eye  covered,  direct  him  to  look 
steadily  with  the  eye  to  be  examined  upon  a  small  mark 
directly  opposite  the  eye.  A  piece  of  chalk  held  in  the 
hand  is  then  to  be  carried  along  the  surface  of  the  board, 
from  its  outer  edge  towards  the  centre,  on  a  vertical  <>r 
horizontal  line,  until  it  can  be  seen  simply  as  a  white 
object :  make  a  mark  at  this  point.  You  will  then  proceed 
to  test  all  the  other  meridians  of  the  blackboard,  with  the 
mark  as  a  centre,  and  place  a  mark  at  each  point  where 
the  chalk  is  first  observed. 

This  record  can  be  easily 

^^^  ^L  transferred  to  a  small  sheet  of 

^t-sdif 
1^B|^^V^  paper,  by  drawing  the  centre 

*$i&  and  the  various  marks  in  their 

V  respective  positions.  Then 
measure  the  distance  in  inches 
from  the  centre  mark  outward 
on  each  meridian,  and  a  line 
drawn  to  connect  each  mark 
will  give  the  size  and  shape  of 
the  visual  field. 

An    excellent    instrument, 
called  the  perimeter,  has  been 
devised  for  testing  the  field  of 
vision.       Invented,    I    believe, 
FIG.  27*. -EMERSON'S  PERIMETER.     by  porster>  also  by  Carmalt  of 

New  Haven,  and  by  Dr.  J.  H.  Emerson  of  this  city.  I 
prefer  Emerson's,  as  I  think  it  is  the  most  perfect  and 
simple.  This  perimeter  consists  of  a  brass  stand,  with 
an  upright,  and  an  arm  one  fourth  of  a  circle  ;  at  the 
end  of  this  arm  there  is  a  half  circle  of  brass,  which  is 
moved  on  the  smaller  arc  by  a  pivot  in  the  centre  ;  in 
this  there  is  an  opening,  through  which  the  person  ex- 
amined must  constantly  look.  This  arc  of  a  circle  is 
graduated  in  degrees,  and  can  be  placed  to  correspond 


EMME  TROPIA .  5  3 

with  any  of  the  meridians  of  the  eye.  A  small  upright 
extends  from  the  stand  for  the  chin  to  rest  upon,  which 
brings  the  eye  exactly  on  a  level  with,  and  in  front  of, 
the  opening  in  the  arc.  There  is  also  a  slide,  moving 
freely  on  the  arc,  from  end  to  end,  on  which  is  placed  a 
small  disc  of  white  paper.  Then,  with  the  person  to  be 
examined  in  the  proper  position,  you  will  make  your  tests 
by  moving  the  slide  on  the  arc  toward  the  centre  until 
the  disc  can  be  seen. 

This  test  will  give  you  the  quantitative  field,  while  a 
small  letter  placed  on  the  disc,  and  used  in  the  same  way, 
will  give  you  the  qualitative  field. 

This  instrument  is  small,  compact,  and  very  useful,  as, 
by  changing  the  white  disc  of  paper  to  one  of  any  other 
color,  we  can  test  the  field  for  its  power  to  distinguish 
•colors  in  all  the  peripheral  parts  of  the  retina.  You  will 
find  that  the  normal  field  varies  in  size  for  the  different 
colors,  as  that  for  white  being  the  largest,  blue  next,  then 
red,  and  that  for  green  the  smallest. 

After  you  have  mapped  out  the  extreme  limits  of  the 
field  of  vision  with  the  perimeter,  you  should  slowly  carry 
the  slide  with  the  disc  completely  up  to  the  centre.  If 
the  white  disc  should  disappear,  or  become  blurred  at  any 
time,  you  must  carefully  record  all  the  points  at  which  the 
blurring  commenced,  and  also  the  points  where  it  becomes 
clear  again,  as  it  is  carried  toward  and  to  the  centre. 
When  you  have  examined  all  the  meridians  and  com- 
pleted your  test,  you  may  find  that  a  certain  portion  of 
the  retina  has  lost  its  sensibility  to  rays  of  light,  though 
the  functions  may  be  perfect  all  around  this  deficient 
portion.  In  this  manner  we  map  out  on  our  diagram  any 
spots  of  deficient  vision  on  the  retina,  as  scotomata,  or 
blind  spots,  from  any  cause,  as  retinal  hemorrhages,  etc. 

I  would  here  particularly  wish  to  caution  you  not  to 
mistake  the  normal  blind  spot,  the  entrance  of  the  optic 


54      LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

nerve,  called  the  punctum  caecum,  or  Mariottcs  blind  spot, 
for  one  of  any  pathological  significance.  There  are  no 
perceptive  elements  at  this  point ;  vision  is  absolutely 
nothing.  The  nerve  entrance  lies  a  short  distance  inside 
of  the  macula,  a  little  below  the  horizontal  meridian.  It 
will  be  found  in  the  field  of  vision  on  the  opposite  side, 
about  15°  outward  and  3°  below  the  point  of  fixation. 

Although  this  blind  spot  is  so  easily  marked  out  with 
the  perimeter,  you  must  remember  that  it  is  very  small, 
and  in  binocular  vision,  as  the  rays  from  any  luminous 
point  enter  each  eye,  they  fall  upon  different  regions  of 
each  retina,  consequently  one  eye  will  supply  any  deficiency 
of  vision,  from  the  rays  falling  upon  the  optic-nerve 
entrance  of  the  other  eye. 

You  will  find  with  the  perimeter  certain  charts  that 
are  excellent  for  recording  the  extent  of  the  field.  As  they 
are  marked  to  show  the  size  of  the  normal  field  and  the 
optic-nerve  entrance,  you  can  readily  record  the  results  of 
your  examination.  By  them,  if  taken  at  different  times, 
you  can  tell  whether  the  field  is  still  contracting,  becom- 
ing larger,  or  of  the  existence  and  extent  of  any  scotomata 
in  the  field  of  vision. 

In  the  use  of  the  perimeter  we  can  place  the  arc  of 
the  circle  at  any  meridian  we  wish  to  test.  It  is  readily 
movable  on  the  centre,  while  at  the  apex  there  is  a  dial 
with  a  pointer,  which  marks  the  meridian  at  which  the  arc 
stands.  In  using  your  test,  either  with  the  white  or  col- 
ored discs,  letters,  or  figures,  these  should  be  moved  from 
the  periphery  of  the  arc  toward  the  centre.  The  mark- 
ings in  degrees,  on  the  back  of  the  arc,  will  show  you  the 
point  at  which  the  white  disc  is  seen.  Generally,  \ve 
examine  the  eyes  in  four  meridians,  as  the  vertical,  hori- 
zontal, and  the  two  intermediate  meridians,  or  at  45°  and 
135°.  But  you  may  examine  any  number  of  meridians 
that  you  may  think  necessary  to  make  your  test  complete. 


EM  ME  TROPIA .  5  5 

As  you  test  each  meridian,  the  other  eye  being  covered 
with  a  screen,  the  point  at  which  the  disc  is  seen  should 
be  marked  on  the  chart.  Now  draw  a  line  from  each 
mark,  and  you  will  have  the  extent  and  shape  of  the  field 
of  vision.  The  usual  extent  of  the  visual  field  will  be 
found  about  90°  outward,  50°  inward,  65°  downward,  and 
45°  upward.  Should  there  be  any  spots  on  the  retina, 
as  scotomata,  they  will  be  marked  out  in  the  same  way, 
when  the  test  is  carried  inward  to  the  centre.  The  reason 
we  find  the  field  limited  on  the  upper  and  inner  part, 
is  because  of  the  projection  of  the  cranial  bones,  as  the 
superior  edge  of  the  orbit  and  the  bridge  of  the  nose. 

You  will  also  note  that,  should  any  contraction  of  the 
field  of  vision  be  shown  by  the  charts,  it  is  the  opposite 
side  of  the  retina  that  is  affected,  the  outer  part  of  the 
field,  as  shown  by  the  charts,  representing  the  inner  part 
of  the  retina.  Now,  should  the  outer  half  of  the  field 
be  blind,  this  is  hemianopsia,  which  would  represent  the 
inner  half  of  the  retina  as  being  affected,  or  hemiopia. 
The  blindness  may  be  in  the  upper  or  the  lower  part  of 
the  field,  as  the  tests  may  show.  You  would  then  have 
the  opposite  parts  of  the  retina  affected  respectively. 

The  emmetropic  eye  will  not  require  glasses,  either 
for  distant  vision  or  for  work  at  near  distances,  as  long  as 
the  power  of  accommodation  and  convergence  is  sufficient ; 
but  in  case  of  failure  of  the  power  of  the  ciliary  muscle, 
our  involuntary  muscle  of  accommodation,  or  of  the  volun- 
tary muscle  of  adduction,  the  internal  recti,  the  eyes  will 
require  external  aids  to  vision.  Or,  we  may  go  still  further, 
and  include  the  negative  part  of  convergence,  according 
to  Landolt,  of  Paris — that  is,  the  power  of  abduction  by 
the  action  of  the  external-recti  muscles.  You  must  remem- 
ber that  the  visual  line  is  fixed  upon  the  object,  not  only 
by  the  action  of  the  internal  recti,  but  also  by  the  con- 
'trolling  antagonistic  muscles,  the  external  recti ;  so  you 


56  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

can  realize  that,  if  these  abducting  muscles  are  too 
weak,  they  also  will  tire  in  the  efforts  to  correct  the  con- 
vergence of  their  antagonistic  muscles. 

We  therefore  find  that,  though  the  emmetropic  eye 
may  be  a  perfect  eye  in  its  refractive  power,  to  so  bend 
parallel  rays  of  light  that  they  will  focus  upon  the  retina 
when  the  eye  is  at  rest,  yet,  if  we  keep  up  a  constant 
strain  upon  the  muscular  power  when  the  eyes  are  at  work 
for  near  vision,  we  must  have  a  certain  power  of  accom- 
modation ;  also  a  perfect  equilibrium  between  the  muscles 
of  adduction  and  abduction.  In  case  these  are  deficient, 
we  must  use  convex  glasses  to  relieve  the  strain  upon  the 
muscle  of  accommodation  ;  and  prisms  to  relieve  the  strain 
on  the  internal-  or  external-recti  muscles. 

We  will  consider  this  more  fully  under  the  subject  of 
accommodation  and  the  use  of  prisms,  with  the  method  of 
testing  the  eyes  for  those  most  important  symptoms  of 
asthenopia  occurring  in  the  emmetropic  eye. 


FOURTH   LECTURE. 

HYPERMETROPIA. 

Hyperopia — Refraction — Direction  of  rays — Vision  of — To  record — Causes  of — 
Manifest — Action  of  ciliary  muscle — Latent  or  concealed — Total — Facultative 
— Relative,  Squint  and  causes — Primary  and  secondary  deviation — Absolute — 
The  punctum  remotum  of — Axial  hypermetropia — Glasses  to  be  ordered. 

GENTLEMEN  : — As  the  normal  or  emmetropic  eye  is, 
when  at  rest,  perfectly  adapted  to  focus  parallel  rays  upon 
its  retina,  there  forming  a  perfect  inverted  image,  let  us 
now  study  the  refraction  of  an  eye  that  is  ametropic,  or 
one  that  will  not  focus  such  rays  when  its  accommodation 
is  at  rest, — one  whose  retina  is  not  situated  at  the  focal 
point  of  the  dioptric  apparatus. 

I  am  inclined  to  believe  that  the  majority  of  eyes  that 
exist  in  nature  are  not  emmetropic,  but  that  when  the 
muscular  system  of  the  eye  is  at  rest  the  rays  of  light  from 
infinity  strike  the  retina  before  they  have  come  to  a  focal 
point,  and  thus  the  images  formed  become  blurred  and 
indistinct.  Such  an  eye  is  called  hypermetropic,  and  the 
condition  of  refraction  hyperopia ;  but  these  terms  are  in- 
terchangeable. The  rays  passing  from  the  retina  outward 
through  the  same  refracting  media,  and  having  the  same 
angle  of  refraction  as  the  emmetropic  eye,  but  coming  from 
a  point  nearer  to  the  refracting  surfaces,  wjll  pass  from 
the  cornea  outward  in  a  divergent  direction.  I  would 
therefore  class  the  hypermetropic  eye  as  one  whose  optic 
axis  is  shorter  than  the  normal,  or  one  in  which  parallel 
rays  are  focused  behind  the  retina,  and  the  emergent 
rays  are  divergent  when  the  eye  is  in  a  state  of  rest. 

57 


58  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

This  condition,  in  which  we  have  a  positive  shortening 
of  the  antero-posterior  diameter  of  the  eye,  is  called  axial 
hypermetropia.  You  will  find  it  to  exist  in  the  majority 
of  those  cases  you  will  examine.  But  you  may  also  find 
that  the  power  of  the  refracting  surfaces  is  not  as  great 
as  in  the  normal  eye,  so  that  the  optic  axis  may  be  of 
normal  length  ;  but  the  curvature  of  the  cornea  or  lens 
being  less  than  that  of  the  normal  eye,  the  parallel  rays 
will  not  focus  until  they  have  passed  behind  the  retina. 
This  condition  is  known  as  refractive  hypermetropia. 
You  will  find  it  very  difficult  to  prove  that  the  re- 
fractive power  is  too  low,  while  the  diagnosis  and  correc- 
tion are  the  same  ;  and  for  the  purpose  of  simplifying  our 
study  of  this  refractive  condition,  we  will  only  consider 
that  variety  in  which  the  optic  axis  is  too  short. 

Now  the  hypermetropic  eye  can  generally  see  as  well 
at  a  distance  as  the  emmetropic  eye,  but  to  do  this  it 
must,  by  the  action  of  the  accommodation,  so  bend  paral- 
lel rays  of  light  that  they  will  exactly  focus  upon  the 
retina. 


FIG.  28. — DIAGRAM  OF  THE  HYPERMETROPIC  EYE. 

This  diagram  represents  an  eyeball  whose  optic  axis 
is  shorter  than  the  emmetropic  eye,  as  from  A'  to  B  ;  the 
parallel  rays  coming  from  infinity  at  C  focus  at  A,  be- 
hind the  retina ;  but  when  the  ciliary  muscle  Y  contracts, 
and  the  refractive  power  of  the  crystalline  lens  D  is  in- 
creased, the  parallel  rays  are  then  focused  at  B,  or  exactly 
upon  the  retina.  If  we  place  a  bi-convex  glass  in  front  of 


HYPERMETROPIA.  59 

the  eye,  it  will  have  the  same  effect  to  focus  the  rays  of 
light  with  the  eye  at  rest,  and  this  glass  will  represent  the 
amount  of  hypermetropia  present. 

If  we  follow  the  course  of  the  rays  of  light  as  they 
proceed  from  the  retina  at  B,  taking  the  region  of  the 
macula  as  the  source  of  illumination,  the  rays  as  they 
pass  outward  through  the  same  media,  having  the 
same  refractive  angle  as  the  rays  passing  inward,  will 
take  a  divergent  direction  as  they  leave  the  cornea,  and 
will  proceed  in  the  direction  of  the  lines  £,  E.  I  wish  to 
impress  this  upon  you,  because,  when  you  estimate  the 
degree  of  hypermetropia  with  the  ophthalmoscope  by  the 
direct  method,  you  must  consider  the  direction  of  these 
emergent  rays.  A  convex  glass  that  will  render  them  paral- 
lel will  represent  the  amount  of  hypermetropia. 

Let  me  illustrate  this  by  an  example  of  a  hyperme- 
tropic  eye  at  rest  when  tested  by  Snellen's  test-type.  The 
eye  can  only  appreciate  the  large  letters  about  -j^-,  but  if 
we  now  place  before  the  eye  a  convex  lens  of  20  inches 
focal  distance,  or  2  D,  the  vision  at  once  becomes  -|-§-,  or 
normal.  Hence  we  see  that  the  hypermetropic  eye  is 
adapted  for  convergent  rays,  because  the  rays  after  pass- 
ing through  the  lens  are  rendered  convergent,  and  then 
exactly  focus  upon  the  retina. 

If  in  place  of  the  convex  lens  the  eye  employs  a  por- 
tion of  its  accommodative  power,  the  V  =  |-{j-.  In  a 
second  case  the  vision  may  be  -§-§-,  and  still  remain  the 
same,  if  we  place  a  convex  lens  before  the  eye  ;  so  that 
we  have  normal  vision  either  with  or  without  a  convex 
lens.  This  latter  is  called  'manifest  hypermetropia,  and 
the  strongest  convex  glass  through  which  vision  still  re- 
mains, J--JJ-,  will  represent  the  amount  of  manifest  hyper- 
metropia (Hm.).  We  would  then  record  this  condition 
of  refraction  as  follows  :  V=f^,  Hm.  -^ ;  that  is  to  say, 
the  V=-|-J,  and  is  still  the  same  when  a  convex  glass  of 
40  inches  focal  distance  is  placed  before  the  eye. 


60  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

As  regards  the  cause  of  hypermetropia,  I  think  I 
have  shown,  in  my  remarks  upon  the  emmetropic  eye,  that 
this  "  flat  formation,"  or  plathymorphia,  is  congenital,  and 
in  some  cases  hereditary.  You  will  remember  as  the 
results  of  the  examinations  made  by  the  late  Dr.  E.  T. 
Ely  on  a  large  number  of  children,  that  they  were  mostly 
hyperopic.  I  will  not  endeavor  to  explain  those  cases 
in  which  the  refractive  power  of  the  dioptric  apparatus 
may  be  too  low,  nor  those  cases  in  which  a  portion  of 
the  refractive  apparatus  may  have  been  removed,  as  after 
cataract  operation  ;  but  while  I  shall  at  some  other  time 
refer  to  the  cases  in  which  there  is  a  failure  of  the  accom- 
modative power,  we  will  now  simply  study  the  eye  as  an 
optical  instrument  whose  focal  distance  is  too  short. 

We  look  at  the  hypermetropic  eye  as  one  whose  optic 
axis  is  too  short,  and  in  which  parallel  rays  will  focus  be- 
hind the  retina,  so  that,  impinging  upon  the  retina,  before 
they  have  reached  a  focal  point,  they  will  there  form 
circles  of  diffusion,  causing  reduced  vision.  But  does  the 
hypermetrope  suffer  from  the  reduced  vision  ?  No  ; 
because  from  the  action  of  the  ciliary  muscle  the  refractive 
power  of  the  eye  is  increased,  and  vision  becomes  perfect. 

We  divide  hypermetropia  into  different  degrees, 
according  to  the  condition  of  the  accommodative  power 
of  the  eye.  This  I  will  illustrate  to  you  by  some  simple 
examples  : 

A  patient  reads  |§,  V  =  i.  Then  if  we  place  a  con- 
vex spherical  glass  before  the  eye,  and  vision  remains  the 
same  f$,  then  the  strongest  convex  glass, — say  +  ^ — that 
will  be  accepted  without  diminishing  vision,  will  represent 
his  manifest  hypermetropia,  which  I  have  shown  you  how 
to  record.  If  we  try  ^V  and  find  the  vision  worse,  we  may 
then  conclude  that  the  amount  of  error  of  refraction  is  at 
least  equal  to  a  glass  of  36  inches  focal  distance.  But 
does  this  equal  the  whole  amount  of  hypermetropia  ? 


H  YPERME  TROPIA .  6 1 

No  ;  because  a  certain  amount  will  be  latent  or  concealed 
from  the  action  of  the  ciliary  muscle,  the  patient  not 
being  able  to  completely  relax  it.  We  must  then  stop  the 
action  of  this  muscle  by  some  mydriatic,  the  best  of 
which  is  the  solution  of  the  sulphate  of  atropia  (4  grs.  to 
an  ounce)  dropped  in  the  eye  several  times,  as  three 
times  a  day,  for  two  days.  Now  we  will  find  that  the 
vision  is  very  much  reduced,  as  the  eye  cannot  focus  the 
rays  of  light  upon  the  retina  then  the  strongest  convex 
glass  that  will  make  the  vision  equal  f&,  will  represent  his 
total  hypermetropia.  We  now  find  that  the  record  stands 
V  =  A'V,  with  +  TV  =  f-jj-,  so  that  a  convex  glass  of  12 
inches  focal  distance  represents  the  amount  of  total  hyper- 
metropia. This  glass  also  shows  you  the  amount  of 
convexity  that  is  added  to  the  crystalline  lens  by  the  action 
of  the  ciliary  muscle,  in  causing  the  parallel  rays  of  light 
to  focus  upon  the  retina. 

From  our  illustrative  case  we  may  conclude  that  the 
manifest  hypermetropia  was  equal  to  -gV,  and  that  the 
total  was  equal  to  TV,  so  that  the  latent  hypermetropia, 
or  the  amount  that  was  concealed  until  we  used  the 
solution  of  atropia,  was  equal  to  (+  iV)  -  -  (+  sV)  =  + 
TV.  This  latent  error  of  refraction  is  necessary  in  some 
cases  to  be  estimated,  particularly  in  young  persons.  Al- 
though the  manifest  amount  is  most  important,  the  latent 
will  show  us  just  how  far  we  may  go  in  making  the 
glasses  for  distant  vision  stronger ;  at  the  same  time  it 
gives  us  a  correct  record  of  the  total  error  of  refraction. 

The  term  facultative  hypermetropia  is  used  by  some 
oculists,  the  meaning  of  which  I  interpret  as  the  faculty 
or  power  of  the  eye  to  see  well  at  a  distance,  either  with 
or  without  a  convex  glass  ;  so  that  it  has  about  the  same 
meaning  as  manifest  hypermetropia.  This  expression  I 
consider  much  more  correct,  because  the  error  of  refrac- 
tion is  manifest,  and  no  other  conditions  of  the  eye  will 


62  LECTURES  ON  THE  ERKOKS  OF  REFRACTION. 

accept  a  convex  glass  and  still  have  V  =  f#,  or  i.  Lan- 
dolt  calls  this  condition  facultative  relative  hypermetropia. 

All  hypermetropes  require  a  certain  amount  of  ac- 
commodation to  see  clearly,  which  is  very  great  in  high 
degrees,  and  it  has  beeri  proven  that  we  can  exert  a 
greater  power  of  the  ciliary  muscle  when  acting  in  con- 
junction with  the  internal  recti.  You  will  notice  some 
hypermetropes  that  can  only  see  clearly  by  converging  the 
visual  axes  to  a  point  much  nearer  than  the  object.  By 
this  means  they  gain  clear  vision  at  the  near  point,  but  at 
the  expense  of  their  binocular  vision.  When  an  object  is 
brought  up  to  a  point  six  inches  from  the  eyes,  the  visual 
lines  are  converged  to  a  point  at  three  inches.  This 
condition  is  called  relative  hypermetropia,  from  the  close 
relation  that  exists  between  the  ciliary  muscle  and  the 
internal  rectus. 

You  will  find  this  condition  in  persons  who  have 
convergent  strabismus,  or  squint.  From  early  childhood, 
when  they  first  begin  to  use  the  eyes,  they  soon  learn  that 
they  can  improve  the  vision  by  squinting ;  and,  although 
the  mother  may  give  you  a  history  of  some  spasm, 
accident,  etc.,  that  occurred  to  the  child  about  the  same 
time,  and  to  which  she  will  attribute  the  cause  of  the 
strabismus,  yet,  when  you  examine  the  eyes  and  find  a 
certain  degree  of  hypermetropia,  you  may  feel  sure  that 
the  refractive  condition  was  congenital,  and  that  the 
strabismus  has  been  acquired  to  enable  the  child  to  see 
its  playthings  clearly. 

At  first,  they  will  not  have  the  squint  constantly,  but  it 
will  always  be  observed  when  the  child  looks  at  near  ob- 
jects, and  occasionally  when  looking  at  a  distance.  This 
condition  is  then  called  periodic  strabismus,  and  can  some- 
times be  relieved  and  corrected  by  the  use  of  a  properly 
selected  glass.  If  not  corrected,  the  strabismus  may  be- 
come permanent  and  the  vision  of  the  squinting  eye  very 


H  YPERME  TROPIA .  63 

much  reduced.  The  image  formed  upon  the  retina  at  the 
macula  lutea  has  been  suppressed  for  so  long  that  the  eye 
becomes  amblyopic,  without  any  obvious  condition  to  ac- 
count for  the  reduced  vision.  After  the  convergent 
squint  has  become  permanent,  it  can  only  be  relieved  by 
a  tenotomy  of  the  internal  rectus,  and  then  correction  of 
the  hypermetropia  with  glasses. 

I  am  inclined  to  think  at  the  present  time,  in  many  of 
the  cases  of  squint  with  hypermetropia,  in  which  we  find 
one  eye  very  amblyopic,  that  probably  there  is  either  a 
deficiency  of  the  retinal  elements  in  that  eye  or  a  non-de- 
velopment of  the  retina.  This  is  usually  of  congenital  ori- 
gin I  believe,  and  not  from  non-use,  as  supposed.  The 
child  or  grown  person  has  never  been  able  to  fix  the 
vision  with  the  squinting  eye.  The  eyes  have  converged 
to  attain  a  larger  amount  of  accommodation,  and  to  enable 
the  eye  with  a  fully  developed  retina  to  see  clearly.  From 
this  congenital  defect  in  vision  the  amblyopic  eye  has  no 
stimulus  to  fix  the  rays  of  light  from  the  object  upon  the 
macula  lutea,  and  so  to  keep  the  visual  lines  parallel  when 
looking  at  a  distance  ;  and  as  the  internal  rectus  muscle 
has  the  greatest  power  of  all  the  external  muscles  of  the 
eye,  it  overcomes  the  action  of  its  antagonist,  and  conse- 
quently the  eyeball  turns  inward  with  convergent  strabis- 
mus established. 

This  deviation  of  the  visual  line  does  not  cause  any 
annoying  diplopia,  or  double  vision,  because  the  squinting 
eye  is  amblyopic,  and  the  retinal  image  of  that  eye  is  very 
indistinct,  consequently  there  is  no  stimulation  to  bring 
the  rays  of  light  upon  the  macula. 

The  direction  of  the  visual  line  of  a  squinting  eye 
from  that  of  the  normal  is  called  the  primary  deviation  ; 
while,  if  the  perfect  eye  is  covered,  so  as  to  force  the 
squinting  eye  to  fix  its  visual  line  upon  the  object,  we  now 
have  a  deviation  of  the  covered  eye  of  the  same  degree 


64  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

as  that  of  the  other.  This  is  called  the  sccondarv  derici- 
tion  ;  or,  in  other  words,  the  squint  is  transferred  to  the 
sound  eye.  Yet,  as  soon  as  the  eyes  are  uncovered,  they 
at  once  resume  the  primary  deviation. 

Let  us  now  consider  the  eye  that  cannot  control  those 
parallel  rays,  or  which  has  lost  its  power  to  bring  them  to 
a  focus  upon  the  retina.  This  condition  generally  occurs 
as  the  patient  nears  the  age  of  forty  years,  but  may  occur 
earlier.  Now  the  hypermetropia  is  positive,  arid  for  this 
condition  we  use  the  term  absolute.  Let  me  illustrate  this 
to  you  by  a  case  that  cannot  see  the  small  letters  at 
20  feet.  When  looking  at  infinity,  the  accommodative 
power  is  too  weak  to  focus  the  parallel  rays  upon  the 
retina,  consequently  they  impinge  upon  the  retina  before 
they  have  come  to  a  focus,  and  there  form  circles  of  dif- 
fusion, requiring  a  much  larger  image  to  appreciate  the 
letters.  Then  we  find  that  V  =  ,'-',"„,  and  the  patient  is 
unable  to  see  clearly  at  a  distance.  If  we  find  that  the 
patient's  V  =  ^L,  then  the  strongest  convex  glass  that 
will  give  the  best  vision  will  represent  the  absolute  hyper- 
metropia, as  V  =  /„%,  with  +  I*  =  |f 

We  have  now,  perhaps,  slight  latent  hypermetropia, 
but  the  refractive  error  is  at  once  shown  and  is  positive  ; 
while  the  amount  of  error  is  represented  by  the  strongest 
convex  glass  that  will  give  the  best  vision,  which  should 
equal  |{[.  Landolt  calls  this  the  absolute  manifest  hyper- 
metropia, as  there  is  always  a  certain  amount  latent. 

This  condition  you  will  seldom  meet  with  in  young- 
people,  but  generally  in  persons  who  have  passed  the 
meridian  of  life.  Their  power  of  accommodation  is  so 
reduced  that  the  eye  cannot  focus  parallel  rays  of  light 
on  the  retina. 

You  will  find  some  cases  of  hypermetropia  that  will 
not  accept  any  convex  glass — that  is,  their  vision  =  '-,\\f 
but  all  convex  glasses  will  blur.  Yet  we  know  that  the  eye 


HYPERMETROPIA.  65 

is  hypermetropic  from  the  examination  with  the  ophthal- 
moscope. The  reason  of  this  is  because  they  have  been 
accustomed  to  use  a  certain  amount  of  accommodation 
when  looking  at  distant  objects  ;  consequently,  when  the 
convex  glass  is  placed  before  the  eye,  they  are  not  able  to 
relax  the  ciliary  muscle.  With  the  convex  glass  the  rays 
are  rendered  too  convergent,  and  the  vision  is  blurred. 

In  such  cases  the  total  hypermetropia  is  all  latent,  and 
can  only  be  demonstrated  by  the  use  of  atropine,  after  the 
condition  of  refraction  has  been  determined  with  the  oph- 
thalmoscope. You  will  frequently  find  this  in  young  per- 
sons, but  in  my  examinations  I  often  make  them  accept 
the  convex  glass,  by  putting  a  glass  over  each  eye,  allow- 
ing binocular  vision,  when  the  accommodation  will  relax 
much  more  readily. 

In  the  emmetropic  eye  we  have  shown  that  its  refrac- 
tion was  adapted  for  parallel  rays  when  at  rest,  conse- 
quently its  punctum  remotum,  or  distant  point  of  distinct 
vision,  would  lie  at  infinity  ;  but  in  the  hypermetropic  eye 
parallel  rays  will  focus  behind  the  retina  in  all  cases,  as 
the  optic  axis  is  too  short.  This  is  the  axial  hyperme- 
tropia of  Prof.  Landolt,  and  the  eye  will  require  convergent 
rays  to  focus  on  the  retina.  We  have  no  convergent  rays 
in  nature, — they  are  parallel  or  divergent  ;  so  the  punctum 
remotum  of  the  hypermetropic  eye  will  lie  behind  the  retina, 
at  the  focal  point  of  the  convergent  rays  (see  A,  fig.  28) 
to  which  the  eye  is  adapted,  and  the  punctum  remotum 
becomes  negative. 

This  negative  point  can  be  found  by  the  focal  distance 
•of  the  convex  glass  that  will  correct  the  total  hyperme- 
tropia, less  the  distance  of  the  glass  from  the  nodal  point 
of  the  eye.  For  example,  if  the  total  amount  of  hyper- 
metropia be  equal  to  a  convex  glass  of  12  inches  focal 
distance,  and  the  lens  be  one  inch  in  front  of  the  nodal 
point,  then  the  punctum  remotum  will  lie  at  1 1  inches  be- 


66  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

hind  the  nodal  point,  which  you  remember  is  near  the 
posterior  surface  of  the  lens  of  the  eye.  The  eye  is 
adapted  for  convergent  rays,  whose  lines  will  intersect  at 
the  punctum  remotum.  When  the  hyperopic  eye  is  at 
rest  the  rays  must  have  this  convergent  direction  to  focus 
on  the  retina,  and  it  consequently  requires  a  part  of  its 
accommodation  to  see  parallel  rays. 

If  we  illuminate  the  fundus  of  the  hypermetropic  eye, 
there  will  be  certain  rays  that  are  reflected  and  pass  out- 
ward. These  rays  will  pass  in  exactly  the  same  direction 
as  rays  that  focus  upon  the  retina  must  take  when  passing 
inward,  as  their  course  is  through  the  same  refractive 
media.  Now  as  we  have  shown  that  the  eye  is  only 
adapted  for  convergent  rays,  consequently  the  rays  pass- 
ing outward  from  the  retina  will  be  divergent  (see  J£,E, 
fig.  28).  They  will  require  a  convex  glass,  equal  to  the 
amount  of  total  hypermetropia,  to  render  them  parallel, 
or  the  same  as  those  passing  from  the  emmetropic  eye. 

As  I  have  stated  that  this  fact  is  important  in  the 
diagnosis  of  hypermetropia  with  the  ophthalmoscope,  I 
must  refer  you  to  the  lecture  on  that  instrument  for  the 
method  by  which  you  may  estimate  the  total  hyperme- 
tropia in  all  cases. 

Having  now  determined  the  amount  of  hypermetropia 
in  any  case  under  our  care,  the  question  arises  :  What 
glasses  shall  we  order  for  this  error  of  refraction  ?  I  have 
found  generally  that  in  young  persons  it  is  only  necessary 
to  correct  the  manifest  hypermetropia,  and  I  would  there- 
fore order  the  strongest  convex  glass  that  they  will  accept 
and  still  have  perfect  vision,  or  the  same  vision  that  they 
have  without  glasses. 

These  glasses  should  be  worn  constantly  for  a  short 
time,  and  then  for  reading  and  other  close  work.  In  those 
cases  where  the  ciliary  muscle  is  too  weak,  and  the  hyper- 
metropia becomes  absolute,  you  will  then  order  the  strong- 


H  YPERME  TROPIA .  67 

est  convex  glass  that  will  make  the  vision  =  -|-g-,  and  have 
this  glass  worn  constantly,  for  both  near  and  distant  vision. 
When  they  have  passed  that  age  when  the  ciliary  muscle 
becomes  too  weak  for  near  vision  with  the  glass  that 
corrects  the  hypermetropia,  then  they  will  require  a 
stronger  glass  for  reading  and  all  near  work. 


FIFTH   LECTURE. 

MYOPIA. 

Axis  too  long — The  myopic  eye — Axial  myopia — Other  causes  than  axial — In- 
creased curvature  of  the  cornea — Commencing  cataract — Congenital  or  ac- 
quired— Causes  and  production  of — Progressive,  with  posterior  staphyloma — 
Diagnosis — With  glasses — Its  punctum  remotum — Emergent  rays — Glasses  to 
be  ordered — Accommodative,  or  spasm  of  ciliary  muscle — Treatment  of  sj 

GENTLEMEN  : — We  have  demonstrated  in  our  previous 
lecture  that  the  eyeball  may  not  have  been  fully  developed, 
and  in  which  the  optic  axis  was  too  short.  Now  we  may 
have  just  the  reverse  of  this  condition,  and  the  eyeball 
will  be  too  long;  /.  e.,  the  optic  axis  will  be  longer 
than  that  of  the  normal  eye.  This  condition  is  called 
myopia,  or  short-sightedness. 

With  the  optic  axis  too  long,  the  rays  of  light  passing 
through  the  same  dioptric  media  as  those  of  the  emmetropic 
eye,  you  will  see  that  the  entering  rays  must  come  to  a 
focus  before  they  reach  the  retina,  and,  crossing,  they  will 
strike  the  retina  in  a  divergent  direction.  They  will  there 
form  circles  of  diffusion,  and  the  images  on  the  retina  will 
be  indistinct.  Then  those  rays  passing  from  the  retina, 
coming  from  a  point  farther  removed  from  the  refractive 
surfaces,  but  having  the  sawc  refractive  angle,  will  pass 
out  of  the  eye  in  a  convergent  direction. 

I  would  therefore  class  the  myopic  eye  as  one  whose 
optic  axis  is  longer  than  that  of  the  normal  eye,  or  one 
in  which  parallel  rays  will  focus  in  front  of  the  retina,  and 
the  emergent  rays  are  always  convergent. 

You  will  find  that  this  condition  exists  in  nearly  all 
cases  of  myopia.  But  there  are  other  conditions  that 

68 


MYOPIA.  69 

may  cause  it.  The  refractive  power  of  the  dioptric  ap- 
paratus may  be  too  strong,  due  to  an  increase  in  the 
normal  curvature  of  the  cornea  or  lens.  The  eyeball 
may  be  of  the  normal  length,  but  owing  to  the  increase 
in  the  refractive  power  the  rays  will  focus  in  front  of  the 
retina. 

Another  remote  cause  you  will  sometimes  see  in  the 
first  stages  of  cataract,  as  a  person  will  then  become  myopic 
or  shortsighted,  though  the  eyes  had  always  hitherto  been 
normal  for  distant  vision.  This  is  due  to  the  changes  that 
are  taking  place  in  the  crystalline  lens,  causing  an  increase 
in  its  size ;  consequently,  as  the  curvature  is  greater, 
so  is  the  amount  of  refraction. 

But  in  the  large  majority  of  cases  you  will  find  that 
there  is  an  actual  increase  in  the  length  of  the  optic  axis  ; 
so  much  so  that  you  will  notice  it  in  the  protruding  eyes 
of  some  patients,  with  somewhat  restricted  movements  of 
the  eyeballs.  This  condition  is  called  by  LANDOLT  axial 
myopia, — an  excellent  term  in  contradistinction  to  the 
myopia  caused  by  an  increase  in  the  power  of  refraction. 

I  prefer  that  we  should  study  the  various  conditions  of 
ametropia  principally  from  the  length  of  the  optic  axis, 
whether  too  long  or  too  short,  as  it  will  simplify  the  study 
of  refraction,  while  we  will  be  able  to  appreciate  the 
course  of  the  rays  of  light  as  they  pass  inward  or  out- 
ward from  the  eyeball  much  more  easily. 

Myopia  is  either  congenital  or  acquired,  as  the  case 
may  be,  though  I  believe  that  there  are  very  few  persons 
born  myopic  except  those  who  may  inherit  it.  While  in 
the  acquired  form,  as  you  will  find  in  many  students,  I 
think  it  is  due  to  the  constant  straining  and  congestion  of 
the  eye,  produced  by  the  dependent  position  of  the  head 
when  a  person  is  leaning  forward  to  read  ;  also  from  the 
constant  pressure  that  is  exerted  upon  the  sides  of  the 
globe  by  the  normal  tension  of  the  ocular  muscles. 


7O  LECl^URES  ON   THE  ERRORS  OF  REFRACTION. 

LANDOLT,  in  his  excellent  work  on  refraction,  has  ad- 
vanced the  theory  that  in  many  cases  the  eye  is  first 
affected  with  a  disease,  such  as  choroiditis  posterior, 
thereby  causing  a  weakness  of  the  tissues  in  the  region  of 
the  macula.  This  may  lead  to  posterior  staphyloma, 
retinal  hemorrhages,  changes  at  the  macula,  and  detach- 
ment of  the  retina.  But  I  am  inclined  to  think  that  the 
condition  of  myopia  previously  existed,  and,  by  the  efforts 
to  see  clearly,  the  existing  pathological  condition  was 
developed,  causing  an  increase  in  the  myopia.  Where 
we  have  this  increase  in  the  myopia  and  the  process  still 
active  we  will  designate  it  as  progressive  myopia,  which 
may  occur  in  an  eye  that  was  at  first  perhaps  emmetropic 
or  hypermetropic. 

We  would  then  have  three  causes  for  the  production 
of  the  myopic  eye :  First,  congenital ;  second,  the 
hypenemia,  or  congestion  from  the  faulty  position  of  the 
head  in  reading  and  study.  This  condition  tends  to 
weaken  the  tissues  of  the  eyeball,  which  are  also  acted 
upon  by  the  constant  drawing  forward  of  the  choroidal 
coat  by  the  fibres  of  the  ciliary  muscle.  Third,  by  the 
constant  intraocular  pressure,  aided  by  the  pressure  of 
the  four  recti  muscles,  upon  the  outer  portions  of  the 
globe.  This  pressure  is  said  by  Landolt  to  be  so  great 
that  by  delicate  manipulation  you  may  feel  the  depressions 
in  the  globe  beneath  the  course  of  the  internal  and  external 
recti  muscles.  I  believe  also  that  this  pressure  is  due 
to  the  constant  tension  produced  by  the  tonicity  of  all  the 
recti  muscles :  as  this  is  exerted  upon  all  parts  of  the 
equator  of  the  globe,  it  must  cause  it  to  give  way,  and 
form  an  ectasia  at  the  weakest  point.  This  point  we  find 
at  the  posterior  pole,  perhaps  already  weakened  by  the 
constant  congestion 'from  the  stooping  position,  or  from  a 
low  degree  of  posterior  sclero-choroiditis,  and  also  because 
this  portion  of  the  globe  is  only  supported  by  the  cushion 


MYOPIA.  71 

of  fat  behind  it,  while  it  is  deprived  anatomically  of  the 
support  of  the  connective  tissue  of  Tenon's  capsule. 

These  last  conditions  existing  in  an  advanced  degree 
give  rise  to  progressive  myopia  that  may  be  decidedly 
pernicious  in  its  results,  as  you  will  find  the  myopia 
constantly  increasing,  until  the  vision  becomes  practically 
useless. 

Now,  how  will  you  determine  that  you  have  a  case  of 
myopia?  First,  the  myope  cannot  bring  parallel  rays  to 
a  focus  upon  the  retina  by  any  effort  at  action  of  the  accom- 
modative muscle,  because  when  the  eye  is  at  rest,  and  the 
ciliary  muscle  fully  relaxed,  with  the  dioptric  media  the 
same  as  in  the  emmetropic  eye,  then  parallel  rays,  as  they 
enter  and  are  refracted,  will  come  to  a  focus  in  front  of 
the  retina.  There  diverging,  they  strike  the  retina  beyond 
the  focal  point,  forming  images  in  circles  of  diffusion.  We 
cannot  reduce  the  refraction  by  any  act  of  accommodation, 
or  make  the  lens  flatter  than  normal.  We  must  then  infer 
that  in  all  cases  the  myopic  eye  cannot  see  clearly  at  a 
distance,  and  that  the  eye  is  not  adapted  for  parallel  rays. 

Let  us  now  resort  to  Snellen's  test.  We  find  the 
smallest  type  that  the  eye  can  see  clearly, — say  y2^- — then 
place  a  concave  glass  before  it,  using  the  weakest  one 
that  will  make  the  vision  equal  •§-$-,  the  number  of  the 
glass — say  yL — will  show  the  amount  of  myopia,  which 
you  will  record  in  this  manner  :  V  =  y2^-,  with  — 

JL_  =  20 
To        ^o- 

Let  us  now  try  the  vision  for  reading,  using  the  finest 
type  and  the  longest  distance,  or  the  punctum  remotum. 
We  find  that  the  patient  can  read  No.  i  of  Jaeger's  type 
at  ten  inches  from  the  eye.  Now  we  know  that  a  concave 
glass  diverges  rays  of  light,  as  if  they  came  from  the 
(negative)  focal  point  of  the  glass.  So  we  find  that  for 
distant  vision  we  must  direct  the  rays  of  light  as  if  they 
came  from  the  most  remote  point  of  distinct  vision  with- 


72  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

out  a  glass — i.  e.,  the  eye  is  adapted  for  rays  from  a  point 
ten  inches  in  front,  and  parallel  rays  must  pass  as  if  they 
came  from  that  point,  when  they  will  focus  upon  the 
retina. 


FIG.  29. — DIAGRAM  OF  THE  MYOPIC  EYE  AND  THE  PUNCTUM  REMOTUM. 

If  we  represent  the  myopic  eye  by  this  diagram,  as  at 
A,  we  will  see  that  the  parallel  rays,  from  infinity  at  C, 
are  brought  to  a  focus  at  B  before  they  reach  the  retina ; 
when  they  reach  the  retina  they  will  form  circles  of  diffu- 
sion at  F  F.  But  with  the  concave  glass  x  placed  before 
the  eye,  we  now  find  that  the  rays,  having  been  rendered 
divergent  as  if  they  came  from  the  point  E,  the  punctum 
remotum,  are  now  exactly  focused  upon  the  retina  at  the 
point  G. 

We  find  the  same  direction  of  the  rays  of  light  when 
the  glass  is  removed  and  the  smallest  test-type  of  Jaeger 
is  placed  at  the  point  E,  ten  inches  in  front  of  the  eye, 
as  shown  by  the  lines.  The  rays  passing  divergently 
from  the  point  E,  and  through  the  refractive  media,  focus 
upon  the  retina  at  G.  We  can  therefore  decide  that  the 
amount  of  myopia  is  shown  by  the  weakest  glass  that  will 
give  the  best  vision  at  twenty  feet ;  or  the  greatest  dis- 
tance  at  which,  in  inches,  the  smallest  type  can  be  read. 

In  your  trial  by  glasses  you  must  always  select  the 
weakest  glass  that  will  give  the  best  vision  ;  for,  if  you  take 
one  of  greater  divergent  power,  you  will  simply  call  the 
accommodation  into  play,  and  as  the  rays  are  rendered 
more  divergent  the  ciliary  muscle  will  contract,  and  we 
still  have  an  exact  focus  upon  the  retina. 


MYOPIA.  73 

Having  seen  that  the  myopic  eye  is  adapted  for 
divergent  rays,  if  now  the  eyeball  be  illuminated,  in  what 
•direction  will  the  return  rays  of  light  pass  outward  ?  If 
we  still  assume  that  our  dioptric  media  is  exactly  the  same 
as  in  the  emmetropic  eye,  then  if  the  rays  proceed  from 
a  point  beyond  the  focal  distance,  and  pass  outward 
through  the  same  refractive  media,  they  have  the  same  re- 
fractive angle,  and  must  become  convergent.  They  will 
then  focus  at  the  same  point  that  represents  the  total 
myopia,  which,  in  the  illustrative  case,  would  be  at  ten 
inches  in  front  of  the  eye.  This  is  shown  in  the  diagram, 
fig.  29,  in  which  the  rays  of  light,  reflected  from  G  and 
passing  outward,  focus  at  E. 

The  myopic  eye  is  said  to  be  the  only  object  in  nature 
that  gives  off  convergent  rays  ;  all  others,  as  you  know, 
being  divergent.  The  hypermetropic  eye  is  the  only  one, 
when  at  rest,  that  is  so  adapted,  or  which  can  adapt  its 
refraction  to  these  convergent  rays  of  light.  Now  if  the 
hypermetrope  will  place  his  eye  so  as  to  receive  the  rays 
coming  from  the  myopic  eye,  then  they  will  focus  upon 
his  retina  (see  Lecture  on  Ophthalmoscopy). 

This  is  a  very  interesting  fact,  and  should  the  degree 
of  ametropia  be  the  same  in  the  eye  of  the  hypermetrope 
as  in  that  of  the  myope,  each  will  be  able  to  see  the  fundus 
without  any  glass,  and  the  degree  of  refraction  in  one  eye 
will  represent  that  of  the  other.  In  making  this  estima- 
tion we  must  calculate  the  distance  of  the  observer's  eye 
from  that  of  the  observed  eye,  and  that  distance  should 
be  added  to  the  amount  of  hypermetropia  of  the  observer, 
provided  his  accommodation  is  at  rest. 

The  next  question  for  us  to  consider  is  this  :  How 
shall  we  order  suitable  glasses  for  cases  of  myopia  where 
there  is  simply  an  elongation  of  the  optic  axis,  without  any 
rapid  increase  in  the  ametropia  ?  This  will  depend  upon 
the  amount  of  error  of  refraction.  In  low  degrees  of 


74  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

myopia,  when  the  vision  equals  f  $,  with  a  glass  of  twenty 
inches  focal  distance  (2  dioptrics),  or  less,  the  patient  will 
need  a  glass  only  for  distant  vision.  The  remote  point  for 
distinct  vision  for  the  smallest  type  is  at  a  distance  of 
twenty  inches  or  more ;  consequently,  by  the  act  of  ac- 
commodation, the  vision  will  be  perfect  at  any  nearer 
point  up  to  the  punctum  proximum. 

Then  if  we  find  that  the  myopia  is  of  a  higher  degree, 
as  4  dioptrics  (ten  inches),  your  patients  will  now  need 
glasses,  not  only  for  the  distant  vision,  but  also  for  read- 
ing. Without  a  glass  they  must  bring  all  type  very  close 
to  the  eye,  that  the  letters  may  be  within  the  punctum 
remotum. 

In  such  cases  I  should  order  the  glasses  that  correct 
the  myopia  at  infinity  to  be  worn  all  the  time.  At  the 
reading  distance  the  glasses  will  only  cause  an  increased 
effort  of  the  accommodation  without  increased  con- 
vergence, and  consequently  less  external  pressure  on  the 
eyeballs  by  the  ocular  muscles. 

That  these  glasses  cannot  possibly  do  any  harm  has 
been  well  proven  in  an  excellent  article  by  Forster  in  the 
"  Archives  of  Ophthalmology,"  where  he  has  noted  the 
effects  on  the  eyes  of  a  large  number  of  persons  who  had 
been  wearing  glasses,  over-correcting  their  existing  axial 
myopia.  Nor  will  these  glasses  cause  the  myopia  to  be 
progressive,  or  produce  the  condition  of  posterior  staphy- 
loma,  from  any  increased  tension  on  the  choroid.  At  the 
same  time  you  must  order  the  weakest  glass  that  will 
make  vision  perfect  at  infinity,  as  too  much  over-correc- 
tion may  cause  symptoms  of  accommodative  asthenopia. 

From  the  above  facts  I  believe  there  is  a  desire  on  the 
part  of  some  oculists  to  fully  correct  the  higher  degrees 
of  myopia,  as  of  12  to  15  dioptrics  ;  but  I  prefer,  in  the 
higher  degrees,  to  endeavor  to  fit  the  glasses  according  to 
the  distance  at  which  the  persons  desire  to  see  clearly. 


MYOPIA.  75 

Let  me  illustrate  this  to  you  by  a  case  in  which  ^  (10 
dioptrics)  is  required  to  make  the  vision  equal  J--2-.  With 
this  glass,  and  the  type  at  the  near  point  or  ordinary 
reading  distance,  as  the  rays  of  light  pass  through  this 
strong  concave  glass  they  will  be  so  divergent  that  it  will 
require  a  severe  effort  of  the  accommodation  to  focus 
the  rays  upon  the  retina.  It  would  then  be  advisable  to 
order  a  much  weaker  glass  for  reading.  In  the  myopic 
eye  we  find  very  few  circular  fibres  in  the  ciliary  muscle, 
and,  consequently,  very  much  diminished  accommodative 
power.  (See  fig.  10.)  It  cannot  stand  the  strain  on  the 
ciliary  muscle  when  wearing  the  glass  that  corrects  its 
total  myopia,  and  so  should  have  a  weaker  glass  for  read- 
ing or  music. 

The  question  is  often  asked  :  Is  not  the  myopic  eye 
of  about  3  D  the  best  eye  for  general  use  through  life, 
for  the  reason  that  in  such  a  case  glasses  will  not  be 
needed  as  old  age  comes  on,  and  the  condition  of  pres- 
byopia will  not  occur?  I  should  answer  that  question  in 
the  negative.  I  am  inclined  to  think  that,  although  a 
myope  of  3  D  will  not  need  a  convex  glass  to  assist  his 
vision  at  the  near  point  when  presbyopia  begins,  the 
refraction  of  his  eye  being  adapted  for  divergent  rays  of 
light  coming  from  a  point  at  its  punctum  remotum,  yet 
he  must  always  wear  glasses  for  distant  vision,  while 
the  emmetrope  will  need  a  glass  only  for  reading.  After 
the  latter  has  passed  the  age  of  forty  years,  his  distant 
vision  remains  perfect  until  very  advanced  age. 

In  those  cases  where  we  have  the  myopic  crescent,  or 
posterior  staphyloma,  so  frequently  seen  in  the  myopic 
eye,  we  may  leave  that  condition  to  pathology  and  the 
diseases  of  the  eye.  But  I  would  say,  when  you  find 
this  condition  extensively  exists,  that  it  is  due  to  a 
low  grade  of  choroiditis  at  the  fundus,  extending  toward 
the  temporal  side.  In  high  degrees  of  progressive  myo- 


76  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

pia  this  staphyloma  is  very  large,  extending  to  the  tem- 
poral side  of  the  disc  one  or  more  diameters.  This 
crescent  can  be  seen  very  perfectly  by  the  indirect  method 
of  examination  with  the  ophthalmoscope.  By  the  direct 
method  the  image  is  so  large  that  only  a  portion  can  be 
seen  at  a  time.  These  cases  will  require  glasses  fitted  in 
the  same  way  as  in  the  healthy  eye,  but  the  vision  is 
always  very  much  reduced  from  the  changes  that  have 
occurred  at  the  region  of  the  macula. 

ACCOMMODATIVE     MYOPIA. 

There  is  a  very  interesting  condition  of  the  eyes  that 
may  exist  in  any  case  of  ametropia,  or  even  in  emmetro- 
pia, — a  condition  of  apparent  myopia,  which  you  must 
look  for  in  all  cases  of  asthenopia,  and  which  you  should 
guard  against,  as,  if  not  relieved  by  proper  treatment,  it 
will  make  the  vision  much  worse  and  increase  the  asthe- 
nopia. I  refer  to  the  condition  of  accommodative  myopia, 
so  called  because  true  myopia  may  be  entirely  absent, 
and  the  axis  of  the  eyeball  even  too  short  or  normal. 
This  condition  of  refraction  is  generally  caused  by  an 
over-strain  of  the  eyes  while  at  any  continuous  work ; 
the  ciliary  muscle  is  kept  in  a  constant  state  of  tension 
until  a  condition  of  clonic  or  even  tonic  spasm  exists,  when- 
ever the  vision  is  used  for  near  or  distant  sight. 

When  the  ciliary  muscle  contracts  we  have  an  increase 
in  the  refractive  power  of  the  crystalline  lens,  so  you  will 
readily  see  that,  if  the  rays  are  converged  by  the  action 
of  the  lens  before  they  reach  the  retina,  you  will  have  the 
same  condition  of  refraction  as  in  axial  myopia,  although 
the  axis  of  the  eyeball  may  be  too  short  (hypermetropia), 
or  normal  (emmetropia),  while  even  the  myopic  eye  may 
be  so  affected. 

We  may  illustrate  this  spasm  of  the  accommodation 
by  the  diagram,  fig.  30,  in  which  A  represents  the  eye- 


MYOPIA.  77 

ball  (normal),  when,  if  the  accommodation  is  at  rest,  we 
find  that  parallel  rays  of  light  coming  from  B  will  focus 
upon  the  retina  at  F.  But  if  we  have  a  clonic  spasm  of  the 
•circular  fibres  of  the  ciliary  muscle  y  y,  with  relaxation  of 
the  zone  of  Zinn  and  increased  curvature  of  the  anterior 
portions  of  the  lens,  changing  it  to  D,  we  then  have  an 
increase  in  the  refractive  power  of  the  dioptric  apparatus ; 
consequently  the  parallel  rays  will  now  focus  at  the  point 
E  before  they  have  reached  the  retina,  and  passing  on- 
ward will  form  circles  of  diffusion  at  H H  upon  the 
.retina,  giving  us  the  condition  known  as  accommodative 
myopia. 


FIG.  30. — DIAGRAM  ILLUSTRATING  SPASM  OF  THE  ACCOMMODATION. 

Owing  to  this  increase  in  the  refractive  power  of  the 
lens  by  the  spasm  of  the  ciliary  muscle  the  refraction  be- 
comes practically  myopic,  and  is  adapted  for  divergent 
rays  ;  but,  when  the  ciliary  muscle  is  relaxed,  emergent 
rays  will  pass  outward,  according  to  the  condition  of 
axial  ametropia  or  emmetropia  that  may  be  present. 

This  condition  usually  occurs  from  overwork,  and  is 
about  the  same  in  each  eye,  with  all  the  symptoms  of 
asthenopia,  as  pain  and  discomfort  in  and  around  the  eyes. 

As  the  clonic  spasm  of  the  ciliary  muscle  exists  when- 
ever the  eyes  are  used  for  distant  as  well  as  for  near  vision, 
you  will  notice  that  the  distant  vision  is  very  much  re- 
duced, that  it  will  not  be  improved  by  convex  glasses, 
and  that  it  will  be  almost  normal  when  a  concave  glass 
is  placed  before  the  eye.  The  myope  will  require  a 


78  LECTUKES  ON  THE  ERRORS  OF  REFRACTION. 

concave  glass  stronger  than  the  positive  condition  of 
axial  myopia  that  may  be  present.  You  will  also  notice 
that  the  region  of  accommodation  is  diminished  ;  but  on 
examination  with  the  ophthalmoscope  the  true  refraction 
of  the  eye  is  found.  This  may  be  emmetropic,  hyperme- 
tropic,  or  of  a  much  less  degree  of  myopia,  than  is  shown 
by  the  weakest  glass  that  gives  the  best  vision. 

In  the  treatment  of  this  condition  you  must  use  a 
strong  solution  of  atropine  (4  grs.  to  the  ounce)  infused 
into  the  eye  three  times  a  day,  until  all  the  symptoms  of 
spasm  have  disappeared  and  the  trial  by  glasses  agrees- 
with  the  examination  by  the  ophthalmoscope  and  reti- 
noscopy.  Then  cause  your  patient  to  wear  the  proper 
glass  that  will  correct  the  existing  error  of  refraction, 
and  you  will  have  relieved  him  of  his  symptoms  of 
spasm  and  of  asthenopia. 

In  some  cases  you  may  find  that  there  is  a  tendency 
to  a  return  of  the  spasm  when  the  eyes  are  used,  even  with 
the  proper  correcting  glasses  ;  if  so,  you  must  again  order 
the  atropine  (2  grs.  to  the  ounce)  to  be  used,  perhaps  for 
one  or  two  months,  until  the  accommodation  remains 
at  rest  when  rays  from  the  punctum  remotum  enter 
the  eye. 


SIXTH   LECTURE. 

OPHTHALMOSCOPY. 

Amaurosis  and  Amblyopia — History  and  description — Conjugate  foci — Loring's 
ophthalmoscope — Valk's  improvement — Emergent  rays — Emmetropia — Rule  for 
examination — Hypermetropia — Rule  for  examination — Myopia — Rule  for  exam- 
ination— Astigmatism — Diagnosis  of — Rules  for  the  examination — The  different 
varieties  of — Influence  of  the  accommodation — The  examiner  may  be  ametropic — 
The  indirect  method. 

GENTLEMEN  : — One  of  the  most  important  aids  to  the 
proper  study  of  the  errors  of  refraction  is  the  use  of  the 
ophthalmoscope.  It  will  not  only  reveal  to  us  the  various 
pathological  conditions  that  may  exist  in  any  part  of  the 
dioptric  media  or  at  the  fundus,  but  it  will  also  give  us  a 
key  to  the  exact  condition  of  refraction,  and  enable  us 
to  estimate  the  total  error  in  the  several  varieties  as 
described. 

Before  the  days  of  ophthalmoscopy  the  diseases  of  the 
interior  of  the  eye  were  totally  unknown,  and  all  deficiency 
in  the  sight,  no  matter  what  the  cause  or  pathological  con- 
dition, received  the  name  of  amblyopia  or  amaurosis, — 
words  that  were  used  without  any  practical  meaning 
whatever.  They  denote  that  the  vision  is  impaired  and 
below  the  normal  standard.  But  they  give  us  no  clue  to 
any  pathological  condition  that  may  exist  in  the  eye,  or  to 
any  error  of  refraction  that  may  reduce  the  vision  below 
the  standard. 

Amaurosis,  according  to  the  Greek  definition,  simply 
means  "  to  render  obscure,"  and  is  now  very  seldom  used ; 
the  term  amblyopia  is  still  used,  in  connection  with  that 

79 


SO      LECTURES  ON  THE  EKKORS  OF  REFRACTION. 

condition  of  reduced  vision  for  which  no  cause  can  be 
assigned  by  the  most  careful  examination  with  the  oph- 
thalmoscope. You  will  frequently  meet  with  cases,  par- 
ticularly in  high  degrees  of  hypermetropia,  where,  even  with 
the  correcting  glass,  you  cannot  bring  the  visual  acuteness 
up  to  the  normal  standard  of  |J,  and  yet,  under  an  examina- 
tion with  the  ophthalmoscope,  you  will  find  the  refractive 
media  and  the  retina  apparently  in  a  perfectly  normal 
condition.  LANDOLT,  of  Paris,  ascribes  this  condition  to  a 
non-development  of  the  retinal  elements,  a  congenital  am- 
blyopia,  as  the  hypermetropic  eye  is  one  that  is  not  fully 
developed — the  length  of  the  optic  axis  will  show  the 
diminished  size.  This  is  a  very  admirable  theory,  and  one 
I  am  inclined  to  adopt.  Others  think  that  this  ambly- 
opia,  as  found  in  the  hypermetropic  eye,  is  due  to  the 
reason  that  the  perceptive  elements  of  the  retina  are  not 
sufficiently  stimulated  and  the  visual  impressions  are  sup- 
pressed, particularly  so  in  relative  hypermetropia.  But  I 
think  you  will  have  one  case  that  points  to  one  theory, 
and  another  that  will  point  the  other  way. 

The  importance  of  a  perfect  understanding  of  the  use 
of  the  ophthalmoscope  in  all  cases  of  refraction  should  be 
fully  appreciated.  To  gain  that  end,  you  should  be  familiar 
with  the  principle  upon  which  it  is  based ;  and  when  you 
have  perfected  yourselves  in  its  use  in  diagnosing  and 
estimating  the  errors  of  refraction,  you  will  then  realize 
how  efficient  it  is  in  the  diagnosis  of  all  diseases  of  the 
dioptric  media  and  retina.  The  estimation  of  the  refrac- 
tion should  be  attended  to  before  we  can  give  a  positive 
opinion  of  the  condition  of  the  fundus. 

It  is  not  my  purpose  to  give  you  an  extended  account 
of  the  history  of  the  ophthalmoscope — for  this  I  would  refer 
you  to  LANDOLT'S  and  DE  WECKER'S  works — nor  of  the 
many  diseases  of  the  fundus  that  are  revealed  by  its  use  ; 
but  I  would  fain  make  these  lectures  of  practical  help  by 


OPHTIIALMOSCOP  Y. 


8 1 


a  description  of  the  instrument  in  its  perfect  form,  as  now 
in  use. 

Invented  by  HELMHOLTZ,  in  1851,  it  consisted  simply 
of  a  mirror,  with  an  opening  in  the  centre,  to  which  the  eye 
of  the  observer  may  be  applied  in  the  path  of  the  return 
rays,  as  they  pass  outward  from  the  eye,  after  the  fundus 
is  illuminated  by  the  reflected  rays  from  the  mirror. 

When  we  look  at  an  eye  the  pupil  appears  perfectly 
black — you  cannot  see  beyond  the  iris  ;  and  yet  we  know 
that  the  lens  and  vitreous  beyond  are  perfectly  transpa- 
rent. You  cannot  see  the  entrance  of  the  optic  nerve,  the 
blood-vessels  proceeding  from  it,  nor  the  beautiful  tape- 
turn  of  the  retina.  How  shall  we  account  for  this?  Sim- 
ply because  we  cannot  place  the  eye  in  the  track  of  the 
return  rays.  We  have  all  noticed  that  the  eye  of  a 
cat  shines  brightly  if  you  approach  it  in  the  dark ; 
particularly  if  you  so  hold  a  light  that  your  own  eyes 
are  shaded.  This  is  because  the  cat's  pupil  is  largely 
dilated  ;  and,  as  the  light  is  reflected  from  the  retina,  the 
pupil  appears  red,  the  natural  color  of  an  illuminated 
retina.  So  it  is  with  the  human  eye,  observed  through 
the  aperture  of  the  ophthalmoscope. 


FIG.  31. — CONJUGATE  FOCAL  POINTS  OF  A  BI-CONVEX  LENS. 

It  is  a  well-known  fact  that  rays  passing  through  a  lens, 
as  described  in  Lecture  II.,  will  take  the  same  course,  no 
matter  which  way  they  pass.  If  you  pass  the  rays  from  a 
candle  placed  in  front  of  a  double-convex  lens,  they  will 
be  refracted  and  will  focus  upon  a  screen  beyond  the  lens  ;; 
now  change  them,  and  place  the  candle  where  the  screen 
was,  and  you  again  find  the  rays  will  focus  at  the  point 
where  the  candle  stood  :  this  is  according  to  the  laws, 
of  the  conjugate  foci. 


82  LECTURES  ON  THE   ERRORS  OF  REFRACTION. 

By  referring  to  the  above  diagram,  fig.  31,  you  will  see 
the  direction  in  which  rays  of  light  pass  through  a  convex 
lens  Y.  According  to  the  laws  of  conjugate  foci  the  angle 
of  refraction  is  always  the  same,  no  matter  at  what  point 
you  place  the  source  of  illumination.  If  we  have  parallel 
rays,  as  a,  a,  a,  a,  they  will  focus  on  the  screen  at  a' ;  then, 
if  we  bring  the  illumination  nearer,  as  at  B,  you  will  find 
the  focal  point  changed  to  the  screen  at  B',  and  so  on.  As 
you  bring  the  illumination  nearer,  the  focal  point  recedes 
until  you  come  to  the  point  D,  when  the  rays,  after  pass- 
ing through  the  lens,  will  now  have  a  direction  parallel  to 
the  points  at  D',  D',  D ',  D'.  In  each  position,  the  angle 
formed  by  the  refraction,  aEa',  or  BEB ',  is  the  same. 
We  may  substitute  the  position  of  the  screen  for  that  of 
the  illumination,  and  the  rays  of  light  will  pass  the  other 
way,  with  the  same  refractive  angle. 

It  is  this  law  of  conjugate  foci  that  forms  the  image 
upon  the  retina,  and  as  the  rays  are  reflected  by  the  reti- 
na they  will  return  to  the  source  of  illumination,  pro- 
vided the  examined  eye  be  emmetropic.  Consequently,  if 
we  would  see  the  fundus  of  the  eye,  we  must  place  our 
own  eye  so  that  the  return  rays  can  enter  and  focus  upon 
the  retina. 

It  is  by  the  use  of  the  ophthalmoscope,  then,  that  we 
can  place  the  eye  in  a  position  to  intercept  those  return 
rays  as  they  pass  outward.  Now  the  pupil  of  the  examined 
eye  appears  of  a  beautiful  orange-red  color,  while  any 
opacities  that  may  obstruct  the  return  rays  at  any  point 
will  appear  to  us  a  black  spot  in  the  pupillary  space, 
whether  situated  in  the  cornea,  the  capsules,  the  lens,  or  in 
the  vitreous. 

The  best  ophthalmoscopes  now  in  use  consist  of  a  sim- 
ple mirror,  having  a  perforation  in  the  centre,  slightly  con- 
cave on  its  surface,  so  that  it  will  concentrate  the  rays  of 
light,  and  make  the  illumination  much  more  brilliant  : 


OPHTHALMOSCOP  Y. 


,  placed  behind  the  mirror,  we  have  a  disc,  containing 
a  series  of  convex  and  concave  lenses,  which  can  be  so  ro- 
tated as  to  bring  the  various  lenses  before  the  aperture  in 
the  centre.  By  this  means  we  cause  the  rays  of  light  as 
they  are  reflected  from  the  re- 
tina of  the  eye  under  exami- 
nation to  pass  in  a  perfectly 
parallel  direction  ;  and,  if  the 
observer's  eye  be  adapted  to 
these  rays,  the  glass  placed  at 
the  aperture  will  give  the  ex- 
isting error  of  refraction  in  the 
subject's  eye. 

Loring's  ophthalmoscope, 
with  the  quadrant  behind  the 
disc  of  glasses,  containing  con- 
cave and  convex  .05  and  16. 
D,  is  undoubtedly  the  best  re- 
fraction instrument.  To  this 
I  have  added  a  rack  and  wheel 
motion,  so  that  the  disc  can  be 
rotated  without  removing  the 
ophthalmoscope  from  the  ex- 
aminer's eye  when  estimating 
refraction.  I  trust  you  will 
find  this  attachment  service- 
able. A  full  account  of  it,  pub- 
lished in  the  Medical  Record, 
vol.  xxxi.,  No.  i  7,  page  478,  is 
as  follows  : 

"In  the  use  of  this  ophthalmoscope  for  several  years 
past,  it  has  seemed  to  me  that  if  some  mechanism  could 
be  devised  whereby  the  various  lenses  might  be  readily 
brought  behind  the  aperture  without  removing  the  instru- 
ment from  the  eye,  the  accommodation  would  more 


84  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

readily  tend  to  relax  in  the  estimation  of  hypermetropia, 
and  that  this  would  be  a  decided  advantage.  With  this 
end  in  view  I  have  devised  this  improvement  to  Dr.  E. 
G.  Loring's  instrument,  as  shown  in  the  cut." 

This  consists  of  a  rectangular  bar,  connecting  the  oph- 
thalmoscope with  the  handle,  somewhat  longer  than  the 
bar  now  in  use.  Upon  this  bar  is  a  slide,  with  the  edges 
roughened  so  that  it  can  be  held  steadily  and  firmly  with 
the  thumb  and  forefinger,  and  is  made  to  pass  freely  up 
and  down.  Passing  upward  from  the  slide  is  a  flat  rack 
of  brass,  having  on  one  side  a  series  of  small  teeth,  which 
act  upon  a  cog-wheel  attached  to  the  disc  containing  the 
lenses.  This  cog-wheel  motion  is  so  set  that  when  the 
slide  is  in  the  middle  of  the  bar  the  aperture  in  the  disc 
will  be  over  the  aperture  in  the  ophthalmoscope. 

It  will  be  readily  seen,  then,  that  in  the  use  of  this 
ophthalmoscope,  by  simply  pulling  the  slide  downward 
will  cause  the  disc  to  rotate  to  the  right,  thus  bringing  the 
convex  glasses  successively  behind  the  aperture  ;  or,  push- 
ing the  slide  upward,  the  concave  glasses  are  similarly 
placed. 

The  small  quadrant  that  contains  the  convex  and  con- 
cave glasses  of  16.  D  and  .o5  D  is  fastened  to  the  seg- 
mented cover  of  the  back  of  the  ophthalmoscope  by  the 
two  small  screws  in  the  centre,  and  when  it  is  to  be  used, 
to  obtain  the  stronger  glasses,  it  is  simply  necessary,  if 
convex  glasses  are  needed,  to  put  the  convex  16.  D  over 
the  aperture,  then  push  the  slide  up  to  the  top  of  the  bar, 
and  as  it  is  pulled  downward  the  convex  combinations 
will  be  successively  placed  behind  the  aperture,  from  -f-  8. 
D  to  -|-  23.  D.  The  same  action  of  the  slide  with  the  - 
1 6.  D,  behind  the  aperture  will  make  all  the  combinations 
between  -  -  9.  D  to  -  -  34.  D,  only  pull  the  slide  down  to 
the  lowest  point  first,  and  then  push  it  up  as  the  stronger 
glasses  are  needed.  The  .05  D  can  be  added  to  any 
glass  in  the  disc,  as  wanted. 


OPHTHALMOSCOPY.  85 

I  am  inclined  to  think  that  by  the  use  of  this  attach- 
ment to  Loring's  ophthalmoscope  our  examination  of  the 
fundus  and  the  estimation  of  the  errors  of  refraction  will 
be  much  more  exact  and  satisfactory,  as  the  ease  with 
which  we  can  bring  the  successive  glasses  before  the  eye 
will  allow  the  examiner's  accommodation  to  become  easily 
relaxed  in  the  estimation  of  hypermetropia,  and  also  to 
more  readily  select  the  weakest  glass  in  the  estimation  of 
myopia. 

Since  I  have  used  the  above  improvement  on  the 
ophthalmoscope  I  learn  that  the  same  motion  was  used 
on  a  single  disc  several  years  ago,  and  reported  in 
Graefe  and  Saemish's  "  Hand-Book  of  Ophthalmology," 
vol.  iii.,  part  i.,  page  135,  but  was  unknown  to  me  until 
after  I  had  perfected  and  used  this  improvement. 

To  understand  fully  the  use  of  the  ophthalmoscope  in 
estimating  the  refraction  of  an  examined  eye,  we  must 
study  closely  the  direction  of  the  emergent  rays.  Having 
rendered  the  fundus  of  an  eye  luminous  by  the  mirror  of 
the  ophthalmoscope,  it  does  not  matter  whether  the  rays 
from  the  mirror  come  to  a  focus  or  not,  so  long  as  they 
will  illuminate  the  retina  sufficiently.  As  the  retina  sends 
outward  rays  of  light,  we  have  a  luminous  point  within 
the  eye.  From  this  point,  as  the  rays  pass  through  the 
dioptric  media,  they  will  be  bent  according  to  the  index 
of  refraction  and  the  curvature  of  the  refracting  surfaces 
which  they  meet  in  their  passage  outward. 

Now  we  have  shown  that  the  rays  of  light  when 
passing  through  a  lens  are  refracted  and  will  always  pass 
backward  in  the  same  way ;  and  that  when  coming  from  a 
luminous  point,  either  nearer  to  or  farther  from  the  nodal 
point  of  a  convex  lens,  they  will  have  the  same  angle,  so 
that  if  the  luminous  point  be  brought  nearer  the  lens  the 
rays  will  pass  beyond  it  in  a  divergent  direction,  and  if 
the  luminous  point  be  removed  beyond  the  focal  distance 


86  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

the  rays  will  then  pass  beyond  the  lens  in  a  convergent 
direction. 

You  will  find  this  fact  of  great  assistance  in  estimating 
refraction,  as*  the  same  law  takes  place  in  the  eye.  In 
the  emmetropic  eye  you  have  seen  that  its  dioptric 
apparatus  is  adapted  for  parallel  rays,  consequently  when 
these  rays  pass  in  the  emmetropic  eye  they  will  exactly 
focus  upon  the  retina  and,  being  reflected,  will  return  in 
the  same  paths,  passing  outward  in  the  same  direction. 
Hence  we  see  that  the  emmetropic  eye  is  not  only 
adapted  for  parallel  rays,  but  also  that  the  emergent  rays 
are  parallel.  If  a  convex  glass  be  placed  at  the  aperture 
of  the  ophthalmoscope  it  will  render  the  rays  convergent, 
so  that  the  retina  cannot  be  seen ;  while,  if  we  place  a 
concave  lens  behind  the  aperture,  it  will  render  the  rays 
divergent,  and  the  retina  can  still  be  seen  by  the  action 
of  the  accommodation. 

We  would,  then,  adopt  this  rule  for  the  diagnosis  of 
emmetropia  with  the  ophthalmoscope,  provided  the  ob- 
server's eye  be  emmetropic  and  the  accommodation  at 
rest,  as  follows  :  The  emmetropic  eye  is  one  that  sends 
outward,  when  illuminated,  parallel  rays,  whose  fundus 
can  -be  distinctly  seen  through  the  aperture,  but  the 
image  of  which  will  be  blurred  by  all  convex  glasses. 

Let  us  now  examine  the  hypermetropic  eye,  or  one  in 
which  the  optic  axis  is  too  short,  but  whose  refractive 
index  is  the  same  as  that  of  the  emmetropic  eye. 

When  we  illuminate  the  hypermetropic  eye  with  the 
ophthalmoscope  we  have  the  return  rays  from  the 
fundus  passing  from  a  point  nearer  the  refracting  surfaces 
than  the  focal  distance  (see  fig.  28,  page  58),  consequently, 
having  the  same  refractive  angle,  the  rays  pass  out  diver- 
gently, and  the  fundus  can  be  distinctly  seen  through  the 
aperture  by  slight  exercise  of  the  accommodation.  Now 
place  a  weak  convex  lens  behind  the  aperture  and  the 


OPHTHALMOSCOP  Y.  87 

fundus  can  still  be  distinctly  seen,  and  the  strongest  con- 
vex lens  by  which  the  details  of  the  fundus  are  clear  and 
distinct  will  represent  the  total  amount  of  hypermetropia 
in  the  observed  eye. 

This  fact  is  very  simple.  Because,  if  the  emergent 
rays  are  divergent,  to  bring  them  to  a  focus  in  the  emme- 
tropic  eye,  with  the  accommodation  at  rest,  you  must 
render  them  parallel  ;  wherefore  you  place  a  convex  lens 
before  your  eye  to  bend  these  divergent  rays  until  they 
become  parallel. 


FIG.  33. — ACTION  OF  A  CONVEX  LENS  ON  THE  EMERGENT  RAYS  OF  HYPERMETROPIA. 

I  would  illustrate  this  by  the  preceding  diagram,  in 
which  A  represents  the  eyeball  with  a  shortened  optic 
axis,  OX,  and  the  emergent  rays  B,  B,  B,  B,  pass  out- 
ward divergent  ;  but  when  passing  through  C,  a  convex 
lens,  they  are  bent  toward  the  focal  point,  yet  only 
sufficiently  to  render  them  parallel,  as  shown  by  the  lines 

-/— *•  j    J--*  y    _/  -*•  j    J  ^  • 

For  hypermetropia  our  rule  would  be  as  follows  :  That 
the  hypermetropic  eye  is  one  which  sends  outward,  when 
illuminated,  divergent  rays,  whose  fundus  can  be  distinctly 
seen  through  the  aperture  by  an  effort  of  the  accommoda- 
tion, and  that  the  strongest  convex  glass  by  which  the 
details  of  the  fundus  are  clear  and  distinct  will  represent 
the  amount  of  total  hypermetropia.  You  will  notice  .that 
in  hyperopia  we  take  the  strongest  glass,  as  you  cannot 
use  one  too  strong  or  over-correct  the  hypermetropia, 


SS  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

because,  when  you  do,  the  image  of  the  retina  in  the 
observed  eye  will  be  blurred. 

Then  you  must  remember,  as  you  estimate  the  refrac- 
tion with  an  ophthalmoscope,  that  you  can  always  see  the 
details  of  the  fundus  clearly  in  hyperopia,  and  with  your 
own  accommodation  relaxed,  the  strongest  glass  which 
will  render  the  emergent  rays  parallel  must  represent  the 
amount  of  total  hyperopia  ;  while  too  strong  a  convex 
glass  will  make  the  emergent  rays  convergent,  and  they 
cannot  be  seen  with  the  emmetropic  eye.  See  the  dotted 
lines  in  fig.  33  ;  the  increase  in  the  power  of  the  'convex 
lens  being  also  shown  by  dotted  lines. 

In  the  myopic  eye,  you  have  one  in  which  the  optic 
axis  is  too  long,  though  the  refractive  index  is  the  same 
as  in  the  emmetropic  eye.  Now,  when  you  illuminate  this 
fundus,  you  have  the  return  rays  coming  from  a  point 
beyond  the  focal  distance  of  the  refractive  surfaces,  and, 
following  the  same  laws,  they  will  pass  outward  in  a  con- 
vergent direction,  and  cannot  be  seen  by  an  emmetrope. 
Place  a  convex  lens  behind  the  aperture,  and  we  will  ren- 
der the  rays  more  convergent  and  the  fundus  more 
blurred  ;  but  if  we  use  a  concave  lens  we  will  cause 
the  emergent  rays  to  pass  outward  in  a  direction  parallel 
to  one  another.  Then  the  weakest  concave  lens  that  will 
render  the  rays  parallel  will  show  the  amount  of  existing 
myopia  in  the  observed  eye.  You  must  remember  to  use 
the  weakest  concave  lens,  because  if  you  use  a  stronger 
glass,  you  will  simply  render  the  rays  of  light  divergent ; 
these  will  then  be  focused  upon  your  retina  by  your 
accommodation,  and  the  amount  of  myopia  will  be  over- 
corrected. 

Our  rule  would  then  be,  for  the  diagnosis  of  simple 
myopia  with  the  ophthalmoscope  as  follows  :  The  myopic 
eye  is  one  that  sends  outward,  or  reflects,  when  illumi- 
nated, convergent  rays,  whose  fundus  cannot  be  distinctly 


OPHTHALMOSCOPY.  89 

seen  through  the  aperture  of  the  ophthalmoscope  with 
the  emmetropic  eye  ;  and  the  weakest  concave  glass  by 
which  the  details  of  the  fundus  can  be  distinctly  seen,  or 
will  render  the  emergent  rays  parallel,  will  represent  the 
total  amount  of  myopia. 


FIG.  34. — THE  MYOPIC  EYE,  ITS  EMERGENT  RAYS,  AND  THEIR  CORRECTION  WITH 

THE  GLASS  F. 

Let  me  illustrate  this  diagnosis  by  the  above  diagram, 
in  which  A  represents  the  myopic  eye,  with  the  optic  axis 
BC  longer  than  normal.  When  we  illuminate  this  eye, 
the  emergent  rays  coming  outward  are  rendered  conver- 
gent, as  they  come  from  a  point  beyond  the  focal  distance 
of  the  refractive  apparatus,  and  will  come  to  a  focus  at 
the  point  E  ;  but  when  passing  through  a  concave  lens,  as 
at  F,  the}/  are  refracted  outward  and  become  parallel, 
D,  D,  D,  D,  and  the  weakest  glass  that  will  produce  this 
effect  will  represent  the  total  degree  of  myopia. 

The  diagnosis  of  the  different  varieties  of  astigmatism 
with  the  ophthalmoscope  are  somewhat  more  difficult, 
although  upon  the  same  principles  which  govern  simple 
hypermetropia  and  myopia.  But  now  we  study  the  emer- 
gent rays  in  the  two  principal  meridians  or  planes  of  the 
eye  ;  always  estimating  the  meridian  nearest  to  the  emme- 
tropic plane  first,  and  remembering  that  these  planes  are 
always  at  right  angles  to  each  other,  though  they  may  be 
at  any  degree  of  the  arc  of  a  circle. 

Should  the  observed  eye  be  a  case  of  simple  hyperme- 


90  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

tropic  astigmatism,  in  which  the  vertical  plane  is  emme- 
tropic  and  the  horizontal  plane  hypermetropic,  you  \vill 
observe  on  examination  with  the  ophthalmoscope  that  all 
the  details  of  the  fundus  are  distinctly  seen  through  the 
aperture,  particularly  all  the  fine  vessels  of  the  optic  disc. 
You  will  remember  that  these  fine  vessels  of  the  disc  will 
always  give  you  excellent  points  for  your  diagnosis  of 
astigmatism.  Now,  if  we  place  a  convex  glass  behind  the 
aperture,  you  will  notice  that  the  horizontal  vessels  be- 
come blurred,  and  that  the  strongest  convex  glass  with 
which  the  vertical  vessels  can  be  clearly  seen  will  represent 
the  amount  of  hypermetropic  astigmatism.  The  correcting 
glass  will  be  a  simple  convex  cylindric  glass  with  the 
axis  vertical.  The  direction  of  the  finer  vessels  that 
can  be  seen  with  the  correcting  glass  will  show  the  direc- 
tion of  the  emmetropic  meridian,  which  in  this  case  would 
be  vertical,  or  at  90°  of  the  arc  of  a  circle/ 

If  we  would  illustrate  this  with  our  diagrams,  let  A 
show  a  section  through  the  vertical  plane,  and  B  a  section 
through  the  horizontal  plane. 


FIG.  35. — THE  EMMETROPIC  PLANE  ;  ENTERING  RAYS,  Ah. 

In  the  diagram  A  you  will  notice  that  the  rays  pass- 
ing inward  will  focus  upon  the  retina ;  while  in  the  dia- 
gram B  they  will  strike  the  retina  before  they  have  come  to 
a  focal  point.  Then  with  these  rays  illuminating  the  fundus, 
and  we  study  the  course  of  the  emergent  reflected  rays, 


OPHTHALMOSCOP  Y. 


FIG.  36. — THE  HYPERMETROPIC  PLANE  ;  ENTERING  RAYS,  Ah. 


FIG.  37. — THE  EMMETROPIC  PLANE  ;  EMERGENT  RAYS,  Ah. 

we  find  that  those  passing  outward  in  the  vertical  or 
emmetropic  plane,  as  in  C,  follow  the  same  paths 
and  emerge  parallel,  while  those  passing  outward 


FIG.  38. — THE  HYPERMETROPIC  PLANE  ;  EMERGENT  RAYS,  Ah. 

in  the  horizontal  plane,  as  shown  in  this  diagram  Dt 
through  a  portion  of  the  cornea,  with  a  lesser  degree 
of  curvature,  are  not  sufficiently  refracted,  and  so  emerge 
divergent.  Such  being  the  case,  you  will  readily  see 


92  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

that  the  vertical  plane  would  be  over-corrected  by  a 
convex  glass,  while  the  horizontal  plane  will  be  made 
emmetropic.  Consequently,  to  correct  this  error  of 
refraction,  we  must  use  a  glass  which  will  only  refract 
rays  of  light  in  the  horizontal  plane  ;  and,  as  the  cylin- 
dric  glass  will  only  refract  rays  at  right  angles  to  its 
axis,  we  must  place  the  axis  of  the  glass  vertical,  or  at  90°. 

Our  rule  for  the  diagnosis  of  simple  hypermetropic 
astigmatism  with  the  ophthalmoscope  would  then  be  :  That 
the  hyperopic  astigmatic  eye  sends  outward  reflected  rays 
in  two  principal  meridians  or  planes  at  right  angles  to 
each  other,  one  being  emmetropic,  the  other  hyperme- 
tropic ;  that  the  emergent  rays  of  the  emmetropic  plane 
are  parallel,  while  those  of  the  hypermetropic  plane  are 
divergent  ;  that  the  strongest  convex  glass  with  which  we 
can  see  the  vessels,  in  any  one  meridian,  will  represent  the 
amount  of  existing  hypermetropic  astigmatism,  and  that 
the  axis  of  the  cylindric  glass  should  be  parallel  with  the 
direction  of  those  vessels  that  are  seen  through  the  cor- 
recting glass.  For  a  more  complete  explanation  of  this 
I  would  refer  you  to  the  lecture  on  astigmatism. 

If  we  now  take  the  example  of  an  eye  in  which  we  have 
the  condition  of  compound  hypermetropic  astigmatism, 
we  must  calculate  the  refraction  of  the  two  principal 
meridians,  in  which  we  find  that  the  amount  of  hyperme- 
tropia  is  greater  in  one  meridian  than  in  the  other.  Then, 
for  example,  let  us  take  the  vertical  and  horizontal 
meridians  as  the  principal  ones,  and  we  shall  find  that  in 
the  vertical  meridian  the  rays  passing  in  parallel  focus 
at  a  point  behind  the  retina,  and  the  rays  passing  in  the 
horizontal  meridian  also  focus  in  the  same  direction  but 
at  a  point  nearer  the  cornea  than  do  those  in  the  vertical 
plane  ;  consequently,  the  emergent  rays  in  the  vertical 
plane  will  be  divergent,  and  those  in  the  horizontal  plane 
will  also  be  divergent,  but  more  positively  than  those  in 


OPHTHALMOSCOP  V.  93 

the  vertical.  It  will  therefore  take  a  stronger  glass  to  ren- 
der the  rays  in  the  horizontal  plane  parallel  than  it  will 
in  the  vertical  ;  and  we  require  a  correcting  convex  glass 
that  will  refract  rays  of  light  in  all  meridians,  but  more  in 
one  meridian  than  in  the  other. 

We  will  make  our  diagnosis  of  compound  hyperme- 
tropic  astigmatism  with  the  ophthalmoscope  in  this  way  : 
On  examination,  the  fine  vessels  of  the  fundus  will  be 
clearly  seen  in  all  directions  unless  a  very  high  degree  of 
hypermetropia  exist,  and  the  strongest  convex  glass  that 
will  render  any  of  the  finer  vessels  of  the  disc  indistinct 
will  represent  the  amount  of  hypermetropia  ;  while  the 
strongest  convex  glass  with  which  the  vessels  in  the  oppo- 
site meridian  can  be  clearly  seen  will  represent  the  amount 
of  hypermetropia  and  astigmatism.  The  direction  of  these 
vessels  will  show  the  axis  of  the  correcting  cylindric 
glass.  If  we  find  that  the  horizontal  vessels  are  rendered 
indistinct  with  a  convex  glass  of  -fa,  or  20  inches  focal 
distance,  and  that  the  vertical  vessels  can  be  seen  with  a 
convex  glass  of  y1^,  or  10  inches  focal  distance,  we  have 
compound  hypermetropic  astigmatism  that  would  be  cor- 
rected by  a  spherical  glass  of  +  ^,  combined  with  a  cylin- 
dric glass  of  +  -^V  axis  90°,  or  vertical. 

Our  rule  for  the  diagnosis  of  compound  hypermetropic 
astigmatism  then  becomes  as  follows  :  That  the  compound 
hypermetropic  astigmatic  eye  is  one  that  sends  outward 
divergent  rays  in  all  meridians,  but  which  are  more  divergent 
in  one  meridian,  or  plane,  than  in  the  other  ;  that  these 
two  principal  planes  are  at  right  angles  to  each  other ; 
that  the  convex  lens  which  renders  the  vessels  in  one 
meridian  indistinct  will  represent  the  amount  of  hyper- 
metropia, that  the  strongest  convex  glass  with  which  we 
can  see  the  vessels  in  the  meridian  at  right  angles,  less 
the  amount  of  hypermetropia,  will  represent  the  amount 
of  hypermetropic  astigmatism  ;  and  that  the  axis  of  the 


94 


LECTURES  ON  THE  ERRORS  OF  REFRACTION. 


•correcting  convex  cylindric  glass  must  be  parallel  with 
those  vessels  that  can  be  seen  with  the  strongest  glass. 

As  in  the  hypermetropic  eye  we  have  less  refracting 
power  in  one  meridian  than  in  the  other  ;  so  we  may  also 
have  in  the  myopic  eye  a  greater  refracting  power  in  the 
different  meridians,  each  of  these  conditions  of  astigmatism 
generally  existing  in  the  curvature  of  the  corneal  surfaces. 

The  most  simple  form  of  this  error  of  refraction  is 
that  of  simple  myopic  astigmatism,  in  which  we  have  the 
refraction  of  one  meridian  emmetropic,  and  that  of  the 
other,  at  right  angles  to  it,  myopic.  In  this  case,  let  us 
see  in  what  direction  the  rays  of  light  pass  inward  and 
outward.  We  again  divide  the  eye  into  two  principal 
planes,  at  right  angles  to  each  other.  Now  as  the  rays 
pass  inward  in  the  vertical  plane,  we  find  they  will  focus 
exactly  upon  the  retina,  as  in  the  diagram  A  ;  while  in  the 


FIG.  39. — THE  EMMETROPIC  PLANE  ;  ENTERING  RAYS,  Am. 


FIG.  40. — THE  MYOPIC  PLANE  ;   ENTERING  RAYS.  Am. 


OPHTHALMOSCOPY.  95 

horizontal  plane  we  find  that,  as  the  curvature  of  the  cornea 
is  greater  than  in  the  vertical,  all  the  rays  will  be  refracted 
with  greater  power,  and  must  focus  in  front  of  the  retina 
as  shown  in  the  diagram  B. 

As  these  rays  of  light  are  reflected  from  the  retina,  we 
will  find  that  the  rays  composing  the  vertical  plane  pass 
outward  in  the  same  direction*  as  they  entered,  and  are 
parallel  after  leaving  the  eye,  as  shown  in  this  diagram  C '/ 


FIG.  41. — THE  EMMETROPIC  PLANE  ;  EMERGING  RAYS,  Am. 

while  the  rays  that  pass  outward  in  the  horizontal 
plane  are  refracted  by  the  increased  curvature  of  the 
cornea  in  that  meridian,  and  consequently  focus  in 
front  of  the  eye.  This  is  shown  in  the  diagram  D. 


FIG.  42. — THE  MYOPIC  PLANE  ;  EMERGING  RAYS,  Am. 

These  emerging  rays  cross  at  a  focal  point  E,  and  now 
diverge.  To  diagnose  this  condition  with  the  ophthalmo- 
scope, we  must  again  study  each  meridian  separately,  and 
so  decide  the  refraction  of  each. 


96  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

When  you  examine  the  fundus  of  an  eye  that  has 
simple  myopic  astigmatism,  you  will  notice  that  the  finer 
vessels  of  the  disc  which  pass  in  certain  directions  are 
indistinct  or  blurred,  according  to  the  degree  of  myopia ; 
while  all  those  vessels  running  in  a  direction  at  right 
angles  are  clear  and  distinct.  Now  if  you  place  a  convex 
glass  behind  the  ophthalmoscope  they  will  all  be  blurred, 
but  if  you  use  a  concave  glass  you  will  find  that  all  the 
vessels  become  clear  in  each  meridian.  The  weakest  glass 
that  will  render  the  blurred  vessels  clear  will  give  you  the 
amount  of  myopic  astigmatism,  and  the  axis  of  the  cor- 
recting cylindric  glass  must  be  placed  at  right  angles  to 
the  vessels  that  appeared  distinct  at  first. 

I  would  illustrate  this  to  you  by  an  example  of  an  eye, 
in  which  you  will  notice  that  through  the  aperture  the 
horizontal  vessels  are  clear  and  well  defined,  while  the 
vertical  vessels  are  indistinct  or  blurred.  Now  if  we  place 
a  concave  glass  of  ^  behind  the  aperture,  this  being  the 
weakest  glass  for  our  diagnosis,  we  find  that  all  the 
vessels  are  perfectly  distinct.  Then,  if  the  axis  of  the 
cylindric  glass  should  be  at  right  angles  to  the  vessels  first 
observed,  we  have  as  the  correcting  glass  a  simple  concave 
cylindric  glass  of  -£$,  with  the  axis  placed  at  90°,  or 
vertical. 

My  rule  for  the  diagnosis  and  estimation  of  simple  my- 
opic astigmatism  with  the  ophthalmoscope  would  then  be 
as  follows  :  That  the  myopic  astigmatic  eye  sends  outward 
reflected  rays  of  light  in  two  principal  meridians  at  right 
angles  to  each  other,  one  being  emmetropic,  the  other 
myopic  ;  that  the  emergent  rays  of  the  emmetropic  plane 
are  parallel,  while  those  of  the  myopic  meridian  are  con- 
vergent ;  that  the  weakest  concave  glass  with  which  \ve 
can  see  the  vessels  in  the  blurred  meridian  will  represent 
the  amount  of  myopic  astigmatism  ;  and  that  the  axis  of 
the  cylindric  glass  should  be  placed  at  right  angles  to  the 


OPHTHALMOSCOPY.  97 

direction  of  the  vessels  which  are  clearly  seen  without  a 


glass. 


These  same  principles  hold  good  in  the  case  of  com- 
pound myopic  astigmatism  ;  but  we  now  have  a  condition 
of  the  elongation  of  the  optic  axis,  with  a  greater  power  of 
refraction  in  one  meridian  of  the  cornea  than  in  the  other. 
Hence,  if  we  measure  the  refraction  of  the  two  principal 
meridians  of  the  eye,  we  will  find  that  in  one  meridian 
there  is  a  certain  amount  of  myopia,  and  in  the  other  a 
still  greater  degree,  with  the  axis  of  the  cylindric  glass  at 
right  angles  to  the  vessels  seen  by  the  weakest  concave 
glass. 

In  what  direction  will  the  rays  of  light  pass  through 
the  dioptric  media,  in  the  two  principal  planes  of  an  eye 
that  has  compound  myopic  astigmatism  ?  In  the  vertical 
plane  we  still  find  that  parallel  rays  will  focus  in  front  of 
the  retina,  and  also  in  the  horizontal  plane.  But  in  one 
plane  the  focal  point  will  be  much  nearer  the  retina  than 
in  the  other,  consequently,  as  the  emergent  rays  in  each 
plane  must  pass  through  the  same  refractive  apparatus, 
but  coming  from  a  point  beyond  the  focal  distance  of  the 
refractive  surfaces,  these  rays  will  pass  outward  in  a  con- 
vergent direction.  Thus  they  have  a  focal  point  for  each 
meridian,  situated  on  the  visual  line,  one  being  nearer  to 
the  eye  than  the  other,  according  to  the  refractive  power 
of  each  plane.  It  is  an  interesting  fact  that  these  emer- 
gent rays  have  two  focal  points  and  an  interval,  the  same 
as  the  "  interval  of  Sturm,"  formed  by  a  convex  spherical 
and  cylindric  lens. 

You  will  also  observe  that,  on  the  examination  of 
the  fundus  with  the  ophthalmoscope,  all  details  are 
blurred,  and  if  you  place  a  weak  concave  glass  behind  the 
aperture  you  will  first  notice  that  certain  vessels  in  one 
plane  become  clear,  and  that  those  at  right  angles  to  them 
are  still  indistinct.  This  glass  will  then  represent  the 


98  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

amount  of  myopia  produced  by  the  elongation  of  the 
optic  axis,  and  should  consequently  be  spherical.  Again, 
place  a  stronger  concave  glass  behind  the  aperture  until 
all  the  vessels  of  the  fundus  come  out  clear,  and  the 
difference  between  these  two  glasses  will  give  you  the 
amount  of  astigmatism,  with  the  axis  of  the  cylindric 
glass  placed  at  right  angles  to  the  direction  of  the  vessels 
first  seen  distinctly. 

Let  us  illustrate  this  in  a  case  where  the  fundus  is 
completely  blurred  in  all  directions.  If  we  now  place  a 
concave  glass  of  -^  behind  the  aperture,  we  shall  see 
clearly  all  the  vessels  that  pass  horizontally,  but  not 
the  vertical  vessels  ;  then  place  a  still  stronger  con- 
cave glass  behind  the  aperture,  as  -fa,  and  the  vessels 
running  vertically  are  now  as  clear  as  the  others. 
If  we  calculate  the  axis  of  the  cylindric  glass  as  at  right 
angles  to  the  vessels  first  seen  clearly,  and  subtract 
the  weaker  glass  from  the  stronger,  we  would  have,  as 
the  correcting  glass  for  this  compound  myopic  astigmatic 
eye,  a  concave  spherical  glass  of  ^,  combined  with  a  con- 
cave cylindrical  glass  of  ^,  with  the  axis  at  90°,  or  vertical. 

Reasoning  from  these  facts  we  therefore  conclude 
that  our  rule  for  the  diagnosis  of  compound  myopic  astig- 
matism should  be  as  follows  :  That  the  compound  myopic 
astigmatic  eye  is  one  which  sends  outward  reflected  rays. 
convergent  in  all  meridians,  but  more  convergent  in  one 
meridian  than  in  the  other ;  that  the  two  principal  planes 
are  at  right  angles  to  each  other ;  that  the  weakest  con- 
cave glass  which  will  make  the  vessel  clear  in  one  meridian 
will  show  the  amount  of  general  myopia,  while  the  weakest 
concave  glass  that  will  render  all  the  finer  vessels  clear 
will  represent  the  amount  of  astigmatism  with  the  axial 
myopia ;  and  that  the  axis  of  the  cylindric  glass  should 
be  placed  at  right  angles  to  the  direction  of  the  vessels 
seen  with  the  weakest  concave  glass.  You  will  note  that 


OPHTHALMOSCOP  Y.  99, 

the  vessels  in  myopia  are  seen  in  the  meridian  of  greatest 
ametropia,  but  that  in  hypermetropia  it  is  just  opposite, 
wherefore  the  axis  of  the  cylindric  glass  must  be  changed. 

We  now  come  to  the  diagnosis  of  the  last  variety  of 
regular  astigmatism  with  the  ophthalmoscope,  where  we 
have  two  distinct  meridians,  at  right  angles  to  each  other, 
and  exactly  opposite  in  their  refraction. 

This  variety  is  called  mixed  astigmatism,  because  we 
have  a  combination  of  the  two  previous  forms  :  one  me- 
ridian will  be  hypermetropic,  while  that  at  right  angles 
to  it  will  be  myopic.  The  simplest  method  to  study  this 
condition  of  refraction  will  be  on  the  supposition  that  the 
retina  is  placed  at  the  same  distance  from  the  cornea  as 
in  the  emmetropic  eye,  but  that  the  curvature  of  the  cor- 
nea is  much  greater  than  normal  in  one  meridian,  and 
much  less  than  normal  in  the  opposite  meridian. 

You  will  readily  understand  that,  as  the  rays  of  light 
from  a  distant  point,  passing  inward  parallel,  will  in  one 
meridian  strike  the  retina  before  they  have  been  brought 
to  a  focal  point,  in  the  meridian  at  right  angles  to  it  the 
rays  will  focus  in  front  of  the  retina.  Consequently  all 
vision  for  distance  will  be  blurred. 

This  can  be  illustrated  by  the  diagrams,  in  which  the 
meridian  of  lesser  curvature  is  shown  at  A,  fig.  43,  where 


FIG.  43. — THE  HYPERMETROPIC  PLANE;  ENTERING  RAYS,  Ahm. 

you  will  notice  that  the  parallel  rays  focus  at  a  point  be- 
hind the  retina,  while  in  fig.  44,  at  B,  you  will  see  that 


100 


LECTURES  ON  THE  ERRORS  OF  REFRACTION. 


FIG.  44. — THE  MYOPIC  PLANE  ;  ENTERING  RAYS,  Ahm. 

they  cross,  and  strike  the  retina  in  a  divergent  direction. 
Now  as  these  rays  of  light  are  reflected  by  the  retina  they 
will  pass  outward  in  each  meridian  with  the  same  refrac- 
tive angle,  but  as  those  which  pass  outward  in  the  hyperme- 
tropic  meridian  will  take  the  direction  as  shown  at  C,  fig. 


FIG.  45. — THE  HYPERMETROPIC  PLANE  ;  EMERGING  RAYS,  Ahm. 

45,  as  they  come  from  a  point  inside  the  focal  distance 
of  the  refracting  surfaces,  consequently  they  must  pass  out 


FIG.  46. — THE  HYOPIC  PLANE  ;  EMERGING  RAYS,  Ahm. 


OPH  THA  LMOSCOP  Y.  I O I 

in  a  divergent  direction  to  F,  F.  But  the  rays  of  light  in 
the  other  meridian,  as  at  D,  fig.  46,  as  they  are  reflected 
by  the  retina,  pass  out  from  a  point  beyond  the  focal  dis- 
tance of  the  refracting  surfaces,  and,  having  a  convergent 
direction,  will  come  to  a  focal  point  at  £,  at  a  distance  from 
the  eye  equal  to  the  amount  of  myopia  in  that  plane. 

The  diagnosis  of  this  condition  of  refraction  with  the 
ophthalmoscope  is  not  one  of  much  difficulty,  as  we  sim- 
ply estimate  the  refraction  of  each  meridian  separately. 
The  appearance  of  the  vessels  at  the  fundus  will  at  once 
impress  upon  us  that  the  eye  is  astigmatic,  and  that  it 
must  be  hypermetropic  in  one  meridian  and  myopic  in 
the  other,  as  you  will  at  once  observe  that  all  the  vessels  in 
one  meridian  are  clear  and  well  defined,  while  all  those  at 
right  angles  to  them  are  very  indistinct. 

I  wish  to  impress  upon  you  that  this  condition 
and  appearance  of  the  fundus  in  a  case  of  mixed  as- 
tigmatism must  be  distinctly  understood.  All  these 
statements  are  made  in  the  belief,  on  my  part,  that 
nearly  all  oculists,  in  the  use  of  the  ophthalmoscope 
for  the  diagnosis  and  estimation  of  refraction,  cannot  con- 
trol their  own  accommodation  so  that  their  ciliary  muscles 
shall  be  perfectly  at  rest.  Hence,  when  I  make  the  state- 
ment that  the  vessels  in  one  meridian  are  clearly  seen 
through  the  aperture,  it  is  because  the  rays  passing  out 
in  the  meridian  at  right  angles  to  that,  and  which  define 
the  edges  of  the  vessels,  are  divergent,  and  by  the  uncon- 
scious action  of  our  accommodation  we  exactly  focus  those 
rays  upon  the  retina,  thus  forming  the  edges  of  the  vessels- 
Now  the  rays  passing  outward  in  the  other  meridian,  of 
greater  curvature,  are  convergent,  and  will  focus  before 
they  reach  our  retina  ;  but,  when  they  do  impinge,  they 
overlap  each  other,  and  so  assist  to  form  the  image  of  the 
vessels  or  lines  that  pass  in  that  meridian. 

If  our  accommodation  were  completely  relaxed,  or  were 


IO2  LECTURES  ON  THE  ERRORS  OF  REFRACTION! 

paralyzed  by  the  action  of  some  mydriatic,  as  atropine, 
then  the  vessels  in  all  directions  would  become  blurred, 
because  we  could  not  focus  the  divergent  rays ;  but,  the 
accommodation  being  active,  the  most  natural  function  of 
the  human  eye  is  to  cause  all  divergent  rays  of  light  to 
exactly  focus  upon  the  retina,  while  in  the  case  of  conver- 
gent rays,  which  is  an  anomaly  of  nature,  we  must  use 
some  means  to  cause  them  to  pass  in  such  a  direction  that 
they  may  focus  upon  the  retina  of  the  observer's  eye. 

How,  then,  shall  we  make  the  diagnosis  and  esti- 
mate the  refraction  in  a  case  of  mixed  astigmatism  ? 
As  we  have  stated,  there  ishypermetropia  in  one  meridian, 
and  myopia  in  the  other  ;  so  we  can  focus  the  rays  of  light 
in  the  hypermetropic  meridian  by  the  act  of  the  accom- 
modation, and  consequently  the  edges  of  the  vessels  pass- 
ing in  the  myopic  meridian  will  be  seen  clearly  and  all 
other  vessels  will  appear  blurred.  " 

In  the  examination  of  the  eye  with  the  ophthalmo- 
scope you  will  see  the  fine  vessels  passing  in  the  same  di- 
rection— say  that  of  the  vertical  meridian.  You  may  have 
this  appearance  of  the  fundus  in  simple  myopic  astigma- 
tism ;  but,  if  you  place  a  convex  glass  at  the  aperture,  and 
the  vessels  are  still  clearly  seen,  you  must  have  mixed 
astigmatism.  Then  the  strongest  convex  glass  with 
which  these  vessels  can  be  seen  will  give  you  the  amount 
of  hypermetropia  in  one  meridian,  and  we  place  the  axis 
of  the  cylindric  glass  parallel  with  the  direction  of  these 
vessels. 

Then  find  the  weakest  concave  glass  with  which  you 
can  see  the  vessels  passing  in  the  opposite  meridian  at 
right  angles  to  the  first,  and  this  will  give  you  the  amount 
of  myopic  astigmatism,  with  the  axis  of  the  concave 
cylindric  glass  at  right  angles  to  the  convex  glass.  You 
will  readily  see  by  this  that,  if  the  vertical  vessels  are  seen 
through  the  aperture,  and  also  with  a  convex  glass  of 


OPHTHALMOSCOP  Y.  1 03 

i  D  while  the  horizontal  vessels  are  only  seen  with  a  con- 
cave glass  of  i  D,  we  have  a  case  of  mixed  astigmatism, 
equal  to  +  i  D,  cyl.  axis  90°,  -  -  i  D,  cyl.  axis  180°. 

Our  rule  then  is  as  follows  :  In  a  case  of  mixed  astig- 
matism the  emergent  rays  have  a  divergent  direction  in 
one  meridian,  and  are  convergent  in  the  meridian  at  right 
angles  to  the  first  ;  then  the  strongest  convex  glass  that 
will  render  the  divergent  rays  parallel  will  give  the  amount 
of  hypermetropia,  and  the  weakest  concave  glass  the 
amount  of  myopia,  with  the  axis  of  the  convex  cylindric 
glass  parallel  to  the  vessels  seen  through  the  aperture,  and 
the  axis  of  the  concave  cylindric  glass  at  right  angles  to 
the  same  vessels. 

I  will  refer  you  to  the  Lecture  on  Astigmatism  for  a 
more  full  explanation  of  the  theory  of  the  action  of  the 
rays  of  light  in  the  diagnosis  of  astigmatism  with  the 
ophthalmoscope,  and  in  which  I  have  explained  the  rea- 
sons why  the  axis  of  the  correcting  cylindric  glass  should 
be  placed  parallel  to  the  vessels  in  hypermetropia,  and  at 
right  angles  to  the  vessels  in  myopia. 

From  the  foregoing  rules,  I  do  not  think  it  necessary 
or  advisable,  to  use  any  cylindric  glasses  on  the  ophthal- 
moscope, as  the  diagnosis  can  be  readily  and  easily  made 
with  the  spherical  glasses  in  the  disc  attached  to  all  good 
ophthalmoscopes. 

There  is  also  another  point  which  you  must  take  into 
consideration  in  the  estimation  of  the  degrees  of  refrac- 
tion with  the  ophthalmoscope — that  is,  the  actual  refrac- 
tion of  the  examiner's  eye  should  he  be  ametropic.  This 
must  be  allowed  for  in  your  estimation  of  the  total  error 
of  refraction,  or  you  must  place  a  suitable  correcting  glass 
at  the  aperture  which  will  adapt  the  examiner's  eye  for 
parallel  rays.  This  is  particularly  necessary,  if  the  exam- 
iner should  happen  to  be  astigmatic.  He  should  have  a 
suitable  glass  that  will  correct  the  astigmatic  curvature, 


104  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

placed  in  a  clip  at  the  aperture,  so   as  to  make  his  eye 
practically  emmetropic. 

Should  the  examiner  be  simply  hyperopic  or  myopic, 
then  he  can  add  or  subtract  the  amount  of  his  own  re- 
fraction to  the  glass  required  to  correct  the  total  error  of 
refraction  by  the  ophthalmoscope.  Thus,  if  the  examiner 
has  a  hyperopia  of  i  D,  he  can  easily  see  the  fundus  of 
a  myopic  eye  of  i  D.  As  the  emergent  rays  of  the 
examined  eye  will  be  convergent,  coming  to  a  focus  in 
front  of  the  eye,  while  the  examiner's  eye,  being  hyper- 
opic, is  adapted  for  rays  that  will  focus  i  D  behind  his 
eye  ;  consequently  the  emergent  rays  from  the  myopic  eye 
will  exactly  focus  upon  the  retina  of  the  examiner's  eye. 

Then  if  the  examined  eye  should  be  myopic,  of  2  D, 
and  the  examiner's  eye  i  D  hypermetropic,  he  will  see 
the  fundus  of  the  examined  eye  with  a  concave  glass  of 
i  D,  as  his  own  refraction  will  neutralize  i  D  of  the 
examined  eye  ;  and  so,  to  get  the  total  amount  of  myopia, 
he  must  add  to  the  glass  used  in  the  ophthalmoscope  the 
amount  of  his  hyperopia,  and  we  have  a  total  myopia 
of  2  D. 

It  is  just  the  same  if  the  examiner  be  myopic,  as  he 
must  use  a  concave  glass  to  correct  his  myopia  ;  but  he 
must  subtract  the  amount  of  his  myopia  from  the  glass 
required  to  see  the  details  of  the  fundus  when  he  ex- 
amines a  myopic  eye,  or  he  must  add  the  amount  if  the 
examined  eye  be  hypermetropic.  Because  if  the  examiner 
be  myopic  i  D,  and  can  see  the  fundus  of  a  hyperopic  eye 
with  a  convex  glass  of  i  D,  he  will  have  a  total  hyper- 
opia of  2  D  ;  while,  should  he  require  a  concave  glass  of 
3  D,  he  will  have  a  myopia  of  only  2  D. 

You  will  see  by  these  diagrams  the  direction  of  the 
rays  of  light,  when  passing  from  one  eye  to  the  other, 
when  the  error  of  refraction  of  one  eye  is  hyperopic  and 
that  of  the  other  myopic,  while  in  the  lower  diagrams 


OPHTHALMOSCOP  Y. 


105 


v 

the   direction   of  the  rays,   after  correction,  is  shown  by 
the  dotted  lines. 


FIG.  47. — RAYS  PASSING  FROM  THE  MYOPIC  TO  THE  HYPERMETROPIC  EYE  ARE 
PARALLEL  IN  THE  SAME  DEGREE  OF  REFRACTION. 

In  this  diagram,  if  A  is  the  eye  of  the  examiner,  and 
B  the  examined  eye,  one  being  hypermetropic  and  the 
other  myopic,  you  will  see  by  the  dotted  lines,  which  rep- 
resent the  emergent  rays  from  the  retina  of  each  eye,  that 
as  they  have  emerged  they  become  parallel  to  each  other, 
and  consequently  the  rays  proceeding  from  one  retina  will 
focus  upon  the  retina  of  the  other  eye  ;  the  refractive 
error  of  each  eye  being  of  the  same  degree,  but  with  one 
eye  myopic  and  the  other  hypermetropic. 


FIG.  48. — THE  CONVEX  GLASS  C  CORRECTS  THE  MYOPIA  WHEN  EXAMINED  BY  THE 
HYPERMETROPE  OF  SLIGHT  DEGREES. 

Now  in  this  diagram  we  have  the  same  condition  of 
refraction,  but  the  examiner's  eye,  A,  has  a  greater  degree 
of  hypermetropia  than  the  examined  eye,  J3,  has  of  myopia  ; 
consequently  the  rays  from  the  examined  eye,  B,  will  not 


106  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

be  sufficiently  convergent  to  focus  upon  the  retina  of  the 
examiner's  eye  when  the  accommodation  is  at  rest,  but 
will  require  a  convex  glass,  C,  to  make  the  rays  from  the 
eye  B  parallel  with  the  emergent  rays  from  the  eye  A, 
so  that  they  will  focus  upon  the  retina.  To  illustrate 
this  :  If  the  eye  B  has  a  myopia  of  i  D,  and  the  eye  A  a 
hyperopia  of  2  D,  then  it  will  only  require  a  convex  glass 
of  i  D  to  render  the  emergent  rays  from  the  examined 
eye  parallel  with  the  emergent  rays  of  the  examiner,  these 
being  the  rays  to  which  the  hyperopic  eye  is  adapted.  The 
same  lens  would  be  required  if  B  was  the  examiner's  eye. 


FIG.  49. — THE  CONCAVE  GLASS  C  CORRECTS  THE  MYOPIA  OF  Low  DEGREES  \\HKN 
EXAMINED  BY  A  MYOPE. 

Again,  in  this  diagram  we  have  the  emergent  rays 
from  both  eyes,  A,  B,  convergent,  but  more  so  in  one 
than  in  the  other,  then  it  will  require  a  concave  glass  to 
make  the  rays  focus  upon  the  retina  ;  but  as  the  rays  pass- 
ing in  the  examiner's  eye  must  be  divergent  and  not  paral- 
lel, as  in  emmetropia,  we  will  require  a  much  stronger 
glass,  so  as  to  render  the  rays  from  the  examined  eye 
divergent,  when  they  will  focus  upon  the  retina  of  the 
examiner.  And  we  subtract  the  amount  of  the  examiner's 
myopia  from  the  glass  used  at  the  aperture,  for  the  total 
myopia  of  the  examined  eye. 

In  the  estimation  of  the  refraction  of  an  eye  with  the 
ophthalmoscope,  you  should  also  regard  the  distance  at 
which  the  instrument  is  held  from  the  examined  eye  ;  as, 


OPHTHALMOSCOP  Y,  I O/ 

although  it  will  not  make  very  much  difference  in  the  low 
degrees  of  refraction,  yet,  when  you  estimate  the  high  de- 
grees, as  10  D,  or  more,  the  distance  at  which  the  ophthal- 
moscope is  held  from  the  examined  eye  must  be  taken 
into  consideration.  You  must  hold  the  ophthalmoscope 
as  close  to  the  eye  as  possible,  even  until  the  instrument 
may  touch  the  supraorbital  ridge ;  and  then,  to  make  your 
examination  scientifically  correct,  you  should  allow  one 
inch,  the  distance  of  the  ophthalmoscope  from  the  nodal 
point.  But  in  all  your  examinations,  place  your  ophthal- 
moscope in  just  the  same  position  as  the  glass  of  a  pair 
of  spectacles  will  be  when  properly  adjusted,  and  then 
your  examination  with  the  ophthalmoscope  will  agree  with 
the  test  by  glasses. 

In  the  high  degrees  of  myopia,  of  2,  3,  or  4  inches, 
when  the  punctum  remotum  lies  at  such  a  short  distance 
from  the  examined  eye,  an  inch  will  make  a  vast  dif- 
ference in  your  calculations,  as  the  fundus  of  the  eye 
can  be  seen  with  a  much  weaker  glass,  when  placed  very 
close  to  the  eye  ;  and  consequently,  if  you  make  your 
examination  at  two  inches  from  the  eye,  your  result 
will  be  an  over-correction,  or  a  much  stronger  glass 
than  the  actual  degree  of  myopia.  If  you  examine  a  myope 
with  the  punctum  remotum,  at,  say,  five  inches  from 
the  eye,  you  must  place  the  glass  of  the  ophthalmoscope 
so  that  its  negative  focal  point  will  agree  with  the  punc- 
tum remotum  of  the  examined  eye  ;  then,  as  the  emergent 
rays  pass  through  the  glass,  they  will  be  parallel.  The 
nearer  the  glass  is  to  the  punctum  remotum,  the  stronger 
must  be  its  refractive  power. 

The  estimation  of  the  errors  of  refraction  by  this 
direct  method  of  examination  is  absolutely  essential  in 
the  fitting  of  glasses,  as  well  as  in  the  study  of  all  the  finer 
details  of  the  fundus.  But  in  very  high  degrees  of  myo- 
pia, where  the  image  is  very  large,  or  where  we  wish 


io8 


LECTURES  ON  THE  ERRORS  OF  REFRACTION. 


to  have  a  more  general  view  of  the  fundus,  I  would 
advise  you  to  use  the  indirect  method  of  examination. 
It  will  be  of  service  to  you,  and  should  be  understood, 
although  its  results  are  so  indefinite  that  you  will  find  it 
serviceable  in  but  few  cases. 

One  of  the  best  and  simplest  explanations  of  this  indi- 
rect method  of  examination  with  the  ophthalmoscope  I 
find  in  "  The  Refraction  of  the  Eye,"  by  Gustavus  Hart- 
ridge,  F.R.C.S.,  third  edition,  and  which  I  take  the  liberty 
to  quote  as  follows  : 

"  By  the  indirect  method  we  obtain  an  inverted  image  of 
the  disk  by  means  of  a  convex  lens  placed  in  front  of 


FIG.  50  (ffartridge). 

the  eye.  In  emmetropia  (fig.  50)  rays  coming  from 
A  emerge  from  the  eye  parallel,  and  are  focussed  by 
the  convex  lens  (C)  at  a,  and  rays  coming  from  B 
are  focussed  at  b ;  so  also  with  rays  coming  from  every 
part  of  AB,  forming  an  inverted  image  of  AB 
at  ba,  situated  in  the  air  at  the  principal  focus  of 
the  bi-convex  lens.  In  hypermetropia  (fig.  51)  the  rays 


Flo.  51  (ffartridge). 

from  A  emerge  divergent ;  so  also,  of  course,  those  from 
B.  If  these  rays  are  continued  backward,  they  will  meet 
behind  the  eye  (at  the  punctum  remotum),  and  there  form 


OPHTHALMOSCOP  Y. 


109 


an  enlarged  inverted  image  (aft)  of  AB.  It  is  of  this 
imaginary  projected  image  that  we  obtain,  by  the  help 
of  the  bi-convex  lens,  a  final  inverted  image  («•/?),  situated 
in  front  of  the  lens  beyond  its  principal  focus.  In  myopia 


FIG.  52  (ffartridge). 

(fig.  52)  the  rays  from  A  and  B  emerge  from  the  eye  con- 
vergent, forming  an  inverted  aerial  image  in  front  of  the 
eye  at  /to,  its  punctum  remotum.  It  is  of  this  image  we 
obtain  with  a  bi-convex  lens,  placed  between  it  and  the 
eye,  a  final  image  (ba)  situated  within  the  focus  of  the  bi- 
convex lens. 

"  With  this  method  we  are  able  to  detect  the  form  of 
ametropia  by  the  changes  which  take  place  in  the  size  and 
shape  of  the  optic  disc,  always  remembering  that  the  in- 
verted image  of  the  disc  produced  by  a  convex  lens  at  a 
certain  fixed  distance  from  the  cornea  is  larger  in  hyper- 
metropia  and  smaller  in  myopia  than  in  emmetropia.  The 
lens  should  be  held  close  to  the  patient's  eye,  and  as  it  is 
gradually  withdrawn,  the  aerial  image  of  the  disc  must  be 
steadily  kept  in  view.  The  rapidity  with  which  any  in- 
crease or  decrease  takes  place  in  the  size  of  this  image 
gives  us  an  indication  of  the  amount  of  the  refractive 
error. 


A 


FIG.  53. — E,   EMMETROPIC  EYE  ;    RAYS  ISSUING  PARALLEL  ;  IMAGE  FORMED  AT 
THE  PRINCIPAL  Focus  OF  LENS,  NO  MATTER  AT  WHAT  DISTANCE  THE  LENS 

IS    FROM  THE  EYE. 


I  10 


LECTURES  ON  THE  EKRORS  OF  REFRACTION. 


"If  no  change  take  place  in  the  size  of  the  image  on 
thus  withdrawing  the  objective,  the  case  is  one  of  emnic- 
tropia,  because  rays  issuing  from  such  an  eye  are  parallel, 
and  the  image  formed  by  the  object-glass  will  always  be 
situated  at  its  principal  focus,  no  matter  at  what  distance 
the  glass  is  from  the  observed  eye  (fig.  53).  As  the  rela- 
tive distance  of  the  image  and  the  object  from  the  lens  is 
the  same,  the  size  of  the  image  will  also  be  the  same. 

"  If  diminution  take  place  in  the  size  of  the  image,  the 
case  is  one  of  hypermetropia  ;  and  the  greater  the  diminu- 
tion, the  higher  is  the  hypermetropia. 

"This  change  in  size  may  be  explained  by  remembering 
that  in  hypermetropia  the  image  of  the  disc  is  projected 
backward,  and  it  is  of  this  projected  image  we  obtain  a 
final  image  with  the  help  of  the  objective.  The  two  dia- 


FIG.  54. — LENS  AT  4  CM. 


FIG.  55. — LENS  AT  12  CM.  ;  H  HYPERMETROPIC  EYE  ;  C  THE  CENTRE  OF  THE  LENS  ; 
AB  IMAGE  ON  RETINA;  ab  PROJECTED  IMAGE;  fta  THE  FINAL  IM\<;K 
FORMED  HV  THE  OBJECTIVE. 

grams  show  images  formed  by  the  object-glass  when  held 
at  4  cm.  and  at  12  cm.  from  the  cornea,  the  latter  image 
being  the  smaller. 

"  The  following  explains  this  :  The  ratio  of  txfi  to  ab 
varies  directly  as  the  length  C  a,  and  inversely  as  the 
length  C  a.  On  withdrawing  the  lens  Cfrom  the  observed 


OP  II THA  LMOSCOP  Y.  Ill 

eye,  C  a  diminishes  and  C  a  increases  ;  therefore  the  ratio 
of  a/3  to  ab  diminishes, — i.  e.,  the  size  of  the  image 
diminishes. 

"If  the  image  become  larger  on  withdrawing  the 
object-glass,  the  case  is  one  of  myopia  ;  the  greater  the 
increase  of  the  image,  the  higher  the  myopia. 

"  This  increase  in  the  size  of  the  image  can  also  be 
explained  with  the  help  of  mathematics,  remembering 
that  in  myopia  an  inverted  image  is  formed  in  front  of 
the  eye,  and  it  is  of  this  we  obtain  an  image  with  a  con- 
vex glass  placed  between  the  eye  and  the  inverted  image, 
which  we  must  regard  as  the  object ;  the  object  and  its 
image  being  both  on  the  same  side  of  the  lens. 

"In  astigmatism  the  disc,  instead  of  appearing  round,  is 
frequently  oval.  If  one  meridian  decrease  while  the  other 
remains  stationary  as  the  objective  is  withdrawn,  it  is  a 
case  of  simple  hypermetropic  astigmatism.  If  the  whole 
disc  decrease  in  size,  one  meridian  diminishing  more  than 
the  other,  it  is  compound  hypermetropic  astigmatism,  the 
meridian  being  most  hypermetropic  which  diminishes 
most. 

"Increase  in  one  meridian,  the  other  remaining  sta- 
tionary, indicates  simple  myopic  astigmatism. 

"  Increase  in  disc,  but  one  meridian  more  so  than  the 
other,  indicates  compound  myopic  astigmatism,  that  me- 
ridian being  most  myopic  which  increases  most. 

"  If  one  meridian  increase  while  the  other  decrease, 
mixed  astigmatism  is  our  diagnosis." 

Such,  gentlemen,  is  the  description  of  the  indirect 
method  given  by  Hartridge,  and  you  will  find  in  some 
cases  that  this  method  will  assist  you  in  confirming  the 
results  of  your  examination  by  the  direct  method. 

In  closing  this  lecture,  let  me  urge  upon  you  the 
importance  of  the  ophthalmoscopic  estimation  of  refraction, 
as  a  means  of  confirming  your  examination  with  the  trial 


f  12  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

glasses.  You  must  learn  to  relax  your  own  accommodation 
completely,  as  well  as  the  convergence  of  your  optic  axes, 
and,  if  not  able  to  do  so,  find  out  how  much  you  can 
relax.  You  should  do  this  by  means  of  some  very  small 
(diamond)  type  placed  at  the  focal  point  of  a  bi-convex 
lens,  at  which  distance  you  should  read  it  easily  through 
the  lens  ;  and  if  you  cannot  completely  relax  your  accom- 
modation, you  may  use  a  concave  lens  that  will  adapt 
your  eye  to  parallel  rays.  You  will  also  find  it  almost 
impossible  to  relax  the  accommodation  in  the  examination 
of  low  degrees  of  hyperopia,  unless  the  student  should  be 
past  the  meridian  of  life ;  but  I  do  not  think  that,  with 
practice,  you  will  have  much  difficulty  in  the  estimation 
of  hypermetropia,  as  you  place  the  convex  glass  at  the 
aperture  of  the  ophthalmoscope. 


SEVENTH   LECTURE. 

MUSCULAR    ASTHENOPIA. 

Primary  and  secondary  position  of  the  eyeball — Axis  of  rotation — Action  of  muscles 
— Diplopia — Insufficiency — Test  for — Strabismus — Convergent — Concomitant — 
Amblyopia  in  squint — Paresis  or  paralysis — Angle  of  strabismus — Test  with  prisms 
— Projection  of  image — Homonymous  diplopia — Crossed  diplopia — Apparent 
squint — Angle  "a" — Objective  examination  for  squint — Test  for  the  angle  of 
strabismus  and  the  angle  "  a" — Periodic  squint — Deviation  of  the  images  in  di- 
plopia— Refraction  of  prisms — Angle  of  deviation — Principal  angle  of  a  prism — 
Table  of  paresis  of  muscles — Insufficiency  or  paresis  of  the  superior  or  the  inferior 
rectus — The  oblique  muscles — Test  with  prisms — To  test  each  muscle — Landolt's 
ophthalmodynamometer — Method  of  using — Ordering  prisms — Decentred  glasses. 

GENTLEMEN  : — You  will  remember  that  in  our  lecture 
on  anatomy  we  found  that  the  eyeball  was  moved  in  dif- 
ferent directions  by  the  action  of  the  ocular  muscles, 
either  singly  or  combined  ;  also  that,  by  the  action  of 
these  muscles,  the  eyeball  was  turned  on  its  centre  of  ro- 
tation, a  point  lying  upon  the  optic  axis  of  the  eye,  about 
14  mm.  behind  the  cornea.  This  is  practically  a  fixed 
point,  around  which  the  outer  portion  of  the  eyeball 
moves  by  the  action  of  the  several  ocular  muscles. 

We  have  also  seen  that  these  six  muscles  form  three 
pairs,  antagonistic  to  each  other,  which,  by  their  inher- 
ent tonicity,  when  in  a  state  of  rest,  tend  to  keep  the 
eyeball  directed  forward,  the  optic  axes  almost  parallel, 
and  at  an  inclination  of  1 5  degrees  below  the  horizontal 
plane,  so  that  the  rays  of  light  from  a  distant  point  fall 
directly  upon  the  macula  lutea.  This  is  called  the  pri- 
mary position.  Then,  with  the  visual  axes  parallel  to  each 
other,  or  converging  toward  any  point,  we  may  move  the 

"3 


114  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

eyes  simultaneously  to  any  other  point.  The  eyes  are 
then  in  the  secondary  position. 

Now  you  will  readily  see  that,  by  the  action  of  the 
ocular  muscles,  both  eyes  must  work  in  unison,  and,  con- 
sequently, should  any  muscle  fail  in  its  duty,  the  visual 
line  of  that  eye  to  which  such  muscle  belongs  will  be 
changed,  and  the  rays  of  light  from  a  given  point  will 
fall  upon  different  parts  of  each  retinal  field.  The  vision 
will  be  very  much  blurred  in  one  eye,  with  distinct  di- 
plopia,  or  double  vision,  and  the  images  separated  accord- 
ing to  the  degree  of  displacement  of  the  optic  axis.  Then 
should  any  of  these  ocular  muscles  become  weak,  or  its 
nervous  supply  be  not  up  to  the  standard  (a  paresis),  one 
eye  will  occupy  the  primary  or  correct  position,  while  the 
other  eye  will  be  moved  in  an  opposite  direction  from  the 
weakened  muscle. 

We  know  that  the  eyeball  turns  around  the  centre  of 
rotation,  but,  as  it  is  moved  in  various  directions,  it  is 
also  turned  on  certain  axes  of  rotation,  each  of  which 
passes  through  this  centre  of  rotation. 

First,  we  have  the  vertical 'axis,  around  which  the  eye  is 
turned  by  the  rectus  internus  and  rectus  externus,  turning 
the  visual  axis  inward  or  outward,  as  the  muscles  may  act 

The  next  axis  lies  in  the  horizontal  plane,  around 
which  the  globe  moves,  and  the  visual  axis  is  directed  up- 
ward or  downward  by  the  action  of  the  superior  and  in- 
ferior rectus.  This  axis  is  not  strictly  transverse,  or 
at  right  angles  to  the  mid-plane  of  the  body  ;  but  its  nasal 
extremity  lies  rather  forward,  so  as  to  form  an  angle  of 
67  degrees  from  the  visual  axis.  From  this  position,  and 
also  as  the  points  of  origin  of  the  rectus  superior  and  in- 
ferior are  much  nearer  the  median  line  of  the  body  than 
their  points  of  insertion  on  the  globe,  they  would  also 
tend  to  act  in  conjunction  with  the  internal  rectus,  so  as 
to  make  the  visual  axes  converge. 


MUSCULAR  ASTHENOPIA.  115 

The  oblique  muscles,  taking  their  point  of  action  from 
the  region  of  the  .inner  canthus,  both  acting  from  points 
on  the  same  line,  would  tend  to  turn  the  eyeball  upon  an 
axis,  the  anterior  extremity  of  which  lies  at  an  angle  of 
37  degrees  outside  of  the  visual  axis.  (See  fig.  6,  page  1 1.) 

You  will  then  understand  that  the  simple  movements 
of  the  ocular  muscles,  acting  singly,  would  tend,  first,  by 
the  internal  and  external  rectus,  to  turn  the  cornea  out- 
ward or  inward  ;  that  the  superior  and  inferior  rectus 
will  direct  the  cornea  upward  or  downward  and  slightly 
inward ;  while  the  action  of  the  superior  and  inferior 
oblique,  rotating  the  globe  on  its  axis,  would  tend  to  turn 
the  cornea,  by  the  superior  oblique,  downward  and  out- 
ward, and  by  the  inferior  oblique  upward  and  outward, 
at  the  same  time  turning  the  globe  on  its  own  axis.  The 
combined  movements  of  any  of  these  muscles  will  tend  to 
turn  the  globe  in  any  direction,  each  eye  acting  in  unison 
with  its  fellow,  and  keeping  the  visual  axes  directed  upon 
a  single  point. 

If,  then,  any  single  muscle,  or  group  of  muscles,  be 
unable  to  keep  the  visual  axes  in  their  proper  position, 
from  weakness  of  the  muscular  structure,  or  a  paresis  of 
its  nervous  supply,  you  will  find  that  the  visual  axes  will 
not  correspond,  that  the  globe  of  one  eye  will  not  move 
as  quickly  and  readily  in  all  directions  as  its  fellow ; 
while  in  paralysis  of  any  of  these  ocular  muscles  there  will 
be  complete  cessation  of  motion,  a  turning  of  the  globe  in 
an  opposite  direction  to  that  of  the  action  of  the  affected 
muscle,  with  consequent  strabismus. 

When  these  muscles  are  weakened  from  any  cause  we 
have  slight  diplopia,  perhaps  only  at  the  reading  distance  ; 
any  deviation  of  the  globe  will  not  be  noticed.  Nor  are 
there  any  obvious  symptoms  of  this  condition  ;  but,  if  we 
have  a  slight  paresis,  or  weakness,  of  any  one  of  the  ocu- 
lar muscles,  not  sufficient  to  cause  squint,  you  can  readily 


Il6  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

see  which  muscle  is  affected  by  causing  the  patient  to  fol- 
low the  movements  of  a  pencil  or  the  finger,  when  held 
at  different  positions,  in  front  of  the  eyes.  Then,  if  any 
muscle  fail  to  act  properly,  the  cornea  will  lag  behind 
the  movements  of  its  fellow  in  the  other  eye. 

Strabismus,  or  squint,  with  or  without  diplopia,  is  the 
most  frequent  and  common  condition  of  insufficiency  of 
the  ocular  muscles.  It  usually  occurs  as  either  a  conver- 
gence or  divergence  of  the  optic  axis,  and  may  be  due  to 
different  causes. 

You  will  remember  that,  when  speaking  of  the  hyper- 
metropic  eye,  and  the  relative  variety  of  hypermetropia, 
we  found  that  many  children  learn  to  squint,  because, 
from  their  high  degree  of  hypermetropia,  they  see 
more  clearly  by  convergence  of  the  visual  axes,  showing 
first  a  periodic  squint,  and  then  a  condition  of  perma- 
nent or  fixed  squint.  This  condition  is  known  as  con- 
vergent concomitant  strabismus,  in  which  the  convergence 
of  the  visual  axes  seems  fixed  in  one  position.  If  the 
right  eye  be  fixed  upon  an  object,  the  left  one  will  be 
turned  inward  ;  and  if  the  left  eye  is  fixed,the  right  will  turn 
inward  ;  but  the  patient  will  always  fix  one  eye  upon  the 
object,  and  keep  the  other  eye  turned  inward  or  outward. 

In  nearly  all  cases  of  fixed  strabismus,  we  have  one  eye 
highly  amblyopic, — it  is  always  the  squinting  eye  ;  while 
the  refraction  of  both  eyes  will  be  hypermetropic,  from  a 
moderate  to  a  high  degree. 

The  cause  of  the  amblyopia  in  the  squinting  eye  is 
still  a  matter  of  doubt ;  at  one  time  it  was  supposed  to  be 
due  to  non-use  of  the  retinal  elements,  and  suppression  of 
the  image  on  the  retina.  This  theory  is  still  held  by  some 
oculists ;  but  I  am  inclined  to  think  that  the  condition  of 
amblyopia  is  congenital,  and  that,  from  the  inability  of  the 
eye  to  fix  its  visual  axis  upon  an  object,  due  to  the  non- 
stimulation  of  the  rays  of  light,  the  eye  turns  inward.  (See 


MUSCULAR  ASTHENOPIA.  1 1/ 

Lecture  on  Hypermetropia.)  No  matter  how  early  in 
life  we  test  the  vision,  we  find  one  eye  more  or  less  am- 
blyopic,  and  no  resultant  improvement  in  the  sight  by  the 
use  of  glasses. 

I  am  led  to  this  conclusion,  because  I  have  seen  some 
cases  of  hypermetropia  in  which  there  was  amblyopia  of 
one  eye,  so  that  the  vision  was  reduced  to  -^-^,  and  no 
improvement  with  glasses  ;  yet  there  was  no  strabismus, 
nor  did  the  ophthalmoscope  reveal  any  evidence  of  abnor- 
mal condition  of  the  retina  or  refractive  media  except 
the  hyperopia. 

We  may  classify  the  causes  of  stabismus  in  three  varie- 
ties :  first,  congenital  amblyopia  ;  second,  relative  hyperme- 
tropia, with  or  without  amblyopia  (amblyopia  ex  anopsia)  ; 
and,  lastly,  paralytic  strabismus,  which  latter  I  hardly  con- 
sider suitable  for  discussion  in  this  work,  though,  should 
it  cause  a  slight  but  annoying  diplopia,  it  may  be  relieved 
by  suitable  prisms. 

Now,  though  we  have  this  convergence  of  the  visual 
axes,  with  a  fixed  squint  in  one  eye,  yet  you  will  notice 
that  the  excursions  of  the  eyes  are  not  diminished,  but 
move  freely  in  all  directions,  unless  there  be  a  paresis,  or 
perhaps  complete  paralysis  of  one  of  the  external  muscles 
of  the  globe. 

Let  us  test  this,  to  see  if  the  movement  of  the  eye  be 
perfectly  normal  in  all  directions.  If  we  cover  one  eye 
with  the  hand  or  a  screen,  the  uncovered  eye  will  readily 
follow  the  movements  of  an  object  in  any  direction.  It  is 
then  evident  that  there  is  no  insufficiency  or  paralysis  of 
the  ocular  muscles,  as  should  there  be  insufficiency  the 
eye  will  lag  behind  in  certain  dire^ejions  ;  while,  should 
there  be  a  paresis,  the  excursions-olf  the  eye  will  be  lim- 
ited ;  and  in  complete  paralysis  the  eyeball  will  not  move 
in  the  proper  direction  through  the  non-action  of  the  par- 
alyzed muscle. 


Il8  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

The  diagnosis  of  fixed  squint  is  quickly  made,  but  in 
the  cases  of  periodic  squint,  or  insufficiency  of  the  ocular 
muscles,  you  must  cover  one  eye  of  the  patient  with  the 
hand  or  a  screen,  and  watch  the  movements  of  the  other 
eye.  But,  to  make  your  examination  correct,  you  may 
measure  the  angle  of  strabismus,  which  Landolt  gives  as 
"  the  angle  which  the  visual  axis  of  the  deviating  eye 
forms"  with  the  direction  it  should  have  in  a  normal 
position." 

To  determine  this  angle  objectively,  Landolt  uses  the 
arc  of  a  perimeter  with  the  deviating  eye  placed  in  the 
centre  of  the  arc,  and  the  other  eye  fixed  on  a  distant  ob- 
ject, as  shown  in  this  diagram. 


FIG.  56. — METHOD  OF  TESTING  THE  ANGLE  OF  STRABISMUS. 

If  the  deviation  of  the  eye  be  in  a  lateral  direction,  we 
place  the  arc  of  the  perimeter  horizontally,  with  the 
deviating  eye  C  in  the  centre  of  the  arc  AB,  and  the 
vision  of  the  other  eye  fixed  upon  the  object  placed  at  the 
point  D.  Then  the  line  CYD  will  be  the  direction  which 
the  visual  line  of  the  squinting  eye  should  have.  If  we 
then  move  a  candle  along  the  arc  from  the  point  Y,  with 


MUSCULAR  ASTHENOPIA.  1 19 

the  eye  of  the  examiner  directly  behind  it,  until  we  can  see 
the  image  of  the  candle  directly  in  the  centre  of  the  cor- 
nea, which  in  this  case  would  be  at  the  point  E,  the  reflec- 
tion being  exactly  at  the  anterior  pole  of  the  eye  and 
upon  the  optic  axis,  then  the  optic  axis  must  be  in  the 
line  CE,  which  forms  an  angle  with  the  proper  direction 
of  the  visual  line.  The  angle  YCE  is  the  angle  of 
strabismus,  and  the  number  of  degrees  on  the  arc  of  the 
perimeter  will  give  us  the  degrees  of  this  angle.  The 
line  CE  is  the  optic  axis,  and  as  the  visual  line  differs  so 
slightly,  we  may  omit  it  from  our  calculation  (see  the  angle 
a),  and  consider  the  optic  axis  and  the  visual  line  as  the 
same. 

Let  us  now  take  up  the  diagnosis  of  those  slight  cases 
of  insufficiency  that  will  cause  fatigue  at  close  work,  or  a 
slight  diplopia  at  both  near  and  far  distances. 

This  condition  is  not  readily  perceptible  to  the  eye,  and 
we  must  depend  upon  our  subjective  examination,  which 
must  be  conducted  by  the  test  with  prisms,  and  upon  the 
statements  of  the  patients. 

You  well  know  that  the  action  of  a  prism  is  to  bend  all 
rays  of  light  toward  the  base.  Then,  if  we  place  a  prism 
of  about  ten  or  twelve  degrees  with  the  base  directly  up- 
ward, before  either  eye,  it  will  deflect  the  rays  of  light 
from  an  object  passing  in  that  eye  so  far  upward  that 
the  rays  will  strike  the  retina  above  the  macula,  and  the 
image  will  be  seen  below,  while  those  passing  in  the 
other  eye  will  strike  upon  the  macula.  As  these  two 
images  will  be  upon  different  parts  of  the  retina  of  each 
eye,  they  will  be  seen,  one  above  the  other. 

Now  having  rendered  the  eye  unable  to  respond  to 
that  stimulus,  the  eyes  have  to  direct  the  visual  axes  to  a 
single  point  by  causing  the  rays  to  fall  upon  different  parts 
of  each  retina  ;  then,  if  there  be  any  weakness  of  either  the 
internal  or  external  recti,  the  object  will  not  only  be  seen 


120  LECTURES  ON  THE   ERRORS  OF  REl-RACTION. 

one  image  above  the  other,  but  you  will  also  find  that  the 
images  are  displaced  laterally,  according  to  the  amount  or 
degree  of  insufficiency  of  the  weakened  muscle. 

We  must  find  out  which  muscle  is  weakened,  and  to 
do  so  we  use  the  flame  of  a  candle  as  our  test,  placed  at 
15  or  20  feet 'distant.  Now  place  a  disc  of  red  glass  over 
one  eye,  making  the  image  of  that  eye  appear  red,  and 
then  notice  in  what  position  the  patient  will  see  the  two 
images  and  the  position  of  the  red  light  when  looking  at 
the  flame  of  the  candle  with  both  eyes. 

If  you  find  that  the  red  light  is  not  only  above,  but  is 
displaced  laterally  and  on  the  same  side  on  which  the  eye  is 
where  you  have  placed  the  red  glass,  we  have  homonymous 
diplopia,  due  to  an  insufficiency  of  the  external  rectus 
muscle  of  one  eye. 

Now,  to  prove  this,  we  know  that  when  the  rays  of 
light  from  the  flame  strike'  the  retina  above  the  hori- 
zontal plane,  they  are  projected  downward,  so  that  the 
image  will  be  seen  below  ;  while  if  the  rays  fall  upon 
the  retina  below  the  horizontal  meridian,  they  will  be  pro- 
jected upward.  Then  if  the  rays  strike  the  retina  outside 
the  vertical  plane,  drawn  through  the  macula,  they  will  be 
projected  inward ;  while  if  they  strike  inside  the  vertical 
plane,  they  will  be  projected  outward. 

If,  then,  we  find  that  the  red  image  is  on  the  same  side 
as  the  eye  over  which  the  red  glass  is  placed,  we  must 
have  an  image  that  is  projected  outward.  To  cause  this, 
the  rays  must  strike  the  retina  inside  the  macula.  Such 
being  the  case,  why  do  the  rays  fall  upon  the  retina  at 
that  point  ?  Because,  as  the  eyeball  turns  upon  its  cen- 
tre of  rotation,  the  posterior  portions  of  the  globe  will 
move  outward  as  the  cornea  moves  inward  ;  and  as 
the  rays  pass  in  straight  lines  they  must  fall  upon  the 
retina  on  the  inside  of  the  macula. 

In  this  diagram   (fig.  57),  which  represents  the  hori- 


MUSCULAR  ASTHENOPIA.  121 

zontal  plane,  with  the  right  eye  at  C,  and  the  left  at 
A,  you  will  notice  that  the  eyeballs  turn  on  their  cen- 
tres of  rotation^'.  If,  then,  the  visual  line  of  the  right 
eye  C  be  fixed  upon  the  light  at  B,  its  visual  line  will  pass 
from  the  macula  m  to  the  light  B ;  but  in  the  left  eye  the 
visual  line  will  be  turned  inward,  as  represented  by  the 
dotted  line  mD,  and  the  rays  of  light  from  the  object 
placed  at  B  must  fall  upon  the  retina  of  the  left  eye  A  at 
the  point  o,  inside  the  macula. 


FIG.  5  7. —DIAGRAM  SHOWING  POSITION  OF  MACULA  :  CONVERGENT  STRABISMUS. 

The  only  muscle,  the  failure  of  whose  action  will  allow 
the  eyeball  to  turn  inward,  is  the  external  rectus ;  so  in 
this  condition  of  homonymous  diplopia  we  must  have  a 
weakness  of  one  of  the  external  recti  muscles. 

Let  us  now  examine  a  case  in  which  the  red  light  is 
seen  by  the  person  upon  the  opposite  side  from  the  eye 
over  which  we  have  placed  the  red  glass.  We  now  have 
crossed  diplopia,  because  the  image  to  the  right  is  seen 
by  the  left  eye,  and  that  to  the  left  by  the  right  eye. 

Then  the  rays  from  one  eye   must  be   projected  in- 


122  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

ward,  so  as  to  make  the  image  on  the  opposite  side  ;  and  if 
so,  the  rays  from  the  candle  flame  must  strike  the  retina 
on  the  outside  of  the  vertical  plane,  drawn  through  the 
macula.  Consequently,  when  the  rays  fall  upon  this  part 
of  the  retina,  the  image  is  projected  inward  and  is  seen  on 
the  opposite  side.  To  produce  this  result,  the  cornea  must 
be  turned  outward,  so  as  to  allow  the  posterior  portions  of 
the  globe  to  rotate  inward. 


FIG.  58. — DIAGRAM  SHOWING  DIRECTION  OF  VISUAL  LINE  :  DIVERGENT  STRABISMUS. 

If  we  look  at  this  diagram  (fig.  58)  in  the  horizontal 
plane,  we  find  that  the  left  eye  is  turned  outward  on  its 
centre  of  rotation  y,  that  the  visual  line  from  m  to  D  is 
turned  the  same  way,  from  the  object  or  light  placed  at 
B,  and  that  the  rays  from  the  point  B  fall  upon  the  retina 
of  the  left  eye  A  at  the  point  o,  outside  the  position  of  the 
macula  m,  while  the  rays  passing  in  the  right  eye  C  fall 
directly  upon  the  macula. 

There  is  only  one  muscle  which  will  allow  the  eyeball  to 
turn  directly  outward,  from  insufficiency  or  paresis,  and 
that  muscle  is  the  internal  rectus,  being  overcome  by  the 
power  of  the  external  rectus.  The  direction  of  the  visual 


MUSCULAR  ASTHENOPIA,  12$ 

line  is  then  outward.  This  condition  must  cause  crossed 
diplopia,  in  which  we  have  an  insufficiency  of  one  of  the 
internal  recti  muscles. 

You  may  meet  with  some  persons  that  have  an  appa- 
rent squint,  but  in  which  the  visual  axis  of  each  eye 
is  fixed  upon  the  object,  while  the  images  are  formed 
upon  the  retina  at  the  macula  lutea ;  although,  from  an 
objective  examination  the  eyes  may  appear  crossed  or 
divergent,  as  regards  the  direction  of  their  optic  axes. 

This  will  be  due  to  the  size  of  the  "  angle  a"  which  is 
formed  by  the  crossing  of  the  optic  axes  and  the  visual 
line,  at  the  nodal  point  of  the  eye. 

The  optic  axic  passes  directly  from  the  centre  of  the 
cornea,  at  the  anterior  pole,  to  the  centre  of  the  back  part 
of  the  globe,  at  the  posterior  pole,  passing  through  the 
nodal  point,  near  the  posterior  surface  of  the  lens  ;  while 
the  visual  axis,  passing  from  the  macula,  through  the 
nodal  point,  to  the  object,  will  cut  the  cornea  inside  the 
anterior  pole. 

Let  us  illustrate  this  by  a  diagram,  in  which  is  repre- 
sented a  horizontal  section  of  an  eyeball. 


FIG.  59. — THE  ANGLE  of. 

The  line  A  B  represents  the  optic  axis,  which  lies 
nearer  to  the  entrance  of  the  optic  nerve  than  the  macula 
lutea,  at  O,  while  the  visual  axis  is  represented  by  the 
line  V  O,  which  passes  from  the  macula  at  O,  through 
the  nodal  point  K,  situated  on  the  optic  axis,  then  through 
the  cornea,  inside  the  anterior  pole  to  the  object  V,  these 


124  LECTURES  ON  THE  EKRORS  OF  REFRACTION. 

two  axes  forming  the  angle  tx,  with  the  apex  at  the 
nodal  point. 

Now  the  position  of  the  macula,  in  reference  to  the  pos- 
terior pole  of  the  eye,  will  limit  the  size  of  the  angle  a,  as 
the  greater  the  distance,  the  greater  will  be  the  size  of  the 
angle.  We  designate  this  angle  by  degrees,  and  when  the 
posterior  pole  lies  between  the  nerve  entrance  and  the 
macula,  as  in  this  instance,  we  call  the  angle  a  positive, 
or  -f  ;  while  in  cases  of  myopia  of  high  degrees,  with 
a  corresponding  increase  in  the  length  of  the  globe,  the 
macula  comes  so  much  nearer  the  nerve  entrance  that  the 
visual  line  passes  out,  through  the  cornea,  on  the  outside 
of  the  optic  axis,  and  the  angle  «  becomes  negative  or  — . 

Now  in  high  degrees  of  hypermetropia  the  angle  a  may 
equal  7°  or  more  ;  while  in  emmetropia  it  is  only  about 
3°,  and  in  myopia  it  is  still  smaller  ;  then  as  we  pass  to  the 
still  higher  degrees  of  myopia,  the  angle  «  disappears, 
until  we  find  it  on  the  inside  of  the  posterior  pole,  when  it 
becomes — ,or  negative.  This  has  been  proved  by  Landolt 
in  the  examination  of  over  one  hundred  eyes  during  life,  and 
from  this  fact  you  will  understand  why  in  certain  cases  of 
refraction  we  may  have  an  apparent  squint,  either  con- 
vergent or  divergent,  of  slight  degrees,  while  both  visual 
axes  are  fixed  upon  an  object.  In  myopia  you  may  have 
an  apparent  convergent  squint,  and  in  hypermetropia  an 
apparent  divergent  squint. 

Let  us  now  diagnose  a  case  of  squint,  and  decide 
whether  we  have  to  deal  with  a  real  squint,  due  to  the 
contraction  or  insufficiency  of  one  of  the  recti  muscles  ; 
or  only  an  apparent  squint,  due  to  the  increased  size  of 
the  angle  a. 

You  will  first  cover  one  eye  of  the  patient  with  the 
hand  or  a  screen,  so  as  to  remove  the  stimulus  of  the 
visual  impressions  on  the  retina  of  that  eye.  Then,  if 
there  be  an  insufficiency  of  any  of  the  ocular  muscles,  the 


MUSCULAR   AST.HENOPIA. 


12$ 


covered  eye  will  turn  in  the  opposite  direction  ;  while,  if 
the  squint  be  only  apparent,  both  eyes  will  remain  in 
their  fixed  position,  as  the  visual  axes  are  directed  to  a 
point  1 8  or  20  inches  in  front  of  the  eyes. 

Should  you  wish  to  be  much  more  exact,  and  decide  just 
how  many  degrees  of  variation  you  may  have  by  the 
angle  a,  or  in  slight  degrees  of  squint  (see  fig.  56),  you 
may  use  the  method  published  by  Landolt's  assistant, 
Charpentier,  in  the  Annal.  d'OcuL,  January,  February, 
1878,  as  follows:  "The  deviating  eye  is  placed  at  the 
centre  of  the  perimeter  (fig.  60),  at  O ;  on  a  line  with  it 
is  placed  a  small  flame,  which  the  patient  must  fix  with 
both  eyes  ;  the  observer  now  moves  along  the  graduated 
arc,  the  flame  remaining  in  its  place,  until  he  sees,  with 
one  eye,  the  reflection  of  the  flame  at  the  apex  of  the 
cornea  of  the  deviating  eye.  The  angle  which  is  thus 
formed  is  double  the  angle  formed  by  the  optic  and  visual 


FIG.  60. — DIAGRAM  SHOWING  THE  ESTIMATION  OF  ANGLE  a. 

axes.     In  this  diagram,  O  is  the  deviating  eye,  which  should, 
in  its  normal  position,  be  directed  toward  L,  but  is  now 


126  LECTURES  ON  THE   ERRORS  OF  REFRACTIOX. 

directed  toward  A  ;  the  angle  A  O  L  is  the  angle  a. 
The  eye  of  the  observer,  at  B,  will  see  the  reflection  of 
the  flame  L  from  the  centre  of  the  cornea,  when  the  ray 
L  C  will  be  reflected  from  the  cornea  at  an  angle  equal 
to  the  angle  of  incidence  L  C  A.  This  last  angle  is  al- 
most the  same  as  the  angle  L  O  A,  which  is  the  angle  of 
the  strabismus,  and  is  one  half  of  the  angle  L  C  B" 

The  angle  a  is  measured  in  the  same  manner.  You 
have  the  examined  eye  in  the  centre  of  the  perimeter,  but 
with  the  visual  line  fixed  upon  the  candle  at  Z,  that  the 
eye  may  see  the  flame  clearly ;  then  the  point  at  which 
the  reflection  of  the  candle  is  seen  on  the  cornea  will  give 
the  position  of  the  anterior  pole,  and  the  direction  of  the 
optic  axis,  a  point  on  the  arc  of  the  perimeter  midway 
between  the  flame  and  the  eye  of  the  examiner.  Then,  if 
the  line  L  O  is  the  visual  line,  and  the  line  A  O  the 
optic  axis,  the  angle  L  O  A  will  represent  the  angle  a, 
which,  expressed  by  degrees,  will  be  one  half  the  distance 
between  the  points  L  and  B  on  the  arc  of  the  perimeter. 

There  are  also  cases  of  strabismus  where  it  is  not 
apparent,  except  when  the  eyes  are  used  for  close  work, 
as  reading,  etc.  This  condition  is  called  periodic  squint, 
and  is  generally  associated  with  relative  hypermetropia. 
We  find  the  vision  perfect  in  one  or  both  eyes,  the  stimu- 
lation of  the  rays  of  light  falling  upon  each  retina  will  be 
great  enough  to  enable  each  eye  to  fix  an  object.  But 
when  either  eye  is  covered  with  the  hand  or  screen,  the 
uncovered  eye  will  turn  inward,  from  the  withdrawal  of 
the  stimulation  of  the  rays.  In  such  cases  you  will  find 
that  the  selection  of  the  proper  glasses,  or  perhaps  a 
slight  tenotomy,  on  the  side  opposite  to  the  weakened 
muscle,  and  on  the  eye  with  diminished  vision,  will 
relieve  all  tendency  of  the  eye  to  converge. 

Marked  strabismus  will  seldom  cause  diplopia,  or  double 
vision,  as  the  rays  that  fall  upon  the  retina  of  the  squint- 


MUSCULAR  ASTHENOPIA. 

ing  eye  form  an  image  upon  the  less  sensitive  parts,  which 
the  patient  soon  learns  to  suppress  ;  but,  in  cases  of  in- 
sufficiency of  any  one  of  the  ocular  muscles,  the  images 
will  be  formed,  one  at  the  macula,  and  another  so  near 
that  region  that  the  double  vision  will  be  very  distressing. 

The  principal  complaint  that  the  patients  will  make  is 
that  the  letters  seem  to  be  double,  with  one  superimposed 
on  the  other,  not  as  they  have  in  asthenopia  from  weak- 
ness of  the  ciliary  muscle,  when  the  letters  all  appear 
blurred  and  indistinct. 

These  slight  cases  of  insufficiency,  or  paresis,  of  the 
ocular  muscles  are  not  so  readily  detected  by  the  objective 
symptoms  that  we  have  been  discussing,  except  at  the  ex- 
treme limits  of  the  field  of  fixation.  You  may  test  them 
in  this  manner  :  You  should  have  the  patient  to  follow  the 
movements  of  a  pencil  held  in  the  hand,  and  moved  in 
every  direction  as  far  as  the  eye  can  possibly  follow  it. 
You  will  then  notice  if  at  any  time  the  eye  wavers  in  its 
movements  at  the  limits  of  the  excursions,  and  if  so,  the 
muscle  which  controls  it  in  that  direction  will  be  the  weak 
or  insufficient  one. 

As  this  simple  test  will  not  answer  in  some  cases, 
you  will  proceed  to  test  them  first  at  the  near  point,  or 
the  reading  distance  of  about  12  to  15  inches.  For  this 
purpose  take  a  piece  of  white  card-board  about  4  by 
8  inches  ;  through  the  centre  of  this  draw  a  line  down- 
ward the  entire  length  of  the  card,  and  in  the  centre  of 
the  line  place  a  round  dot  about  one-fourth  of  an  inch  in 
diameter.  Now  place  a  prism  of  12°,  with  the  base  up- 
ward, over  one  eye,  and  hold  the  card  so  that  the  line  will 
be  vertical,  and  in  the  median  line  of  the  face.  The  patient, 
if  there  be  no  insufficiency,  will  see  only  one  long  line ; 
but  with  two  dots  the  internal  and  external  recti  will  tend 
to  keep  the  vertical  plane  of  each  eye  in  its  primary 
position. 


128  LECTURES  ON  THE  ERRORS  OI-~  KKI-KACTION. 

i 

Now,  if  we  find  that  the  person  sees  two  dots  and  two- 
lines,  it  is  very  evident  that  either  the  external  or  the 
internal  rectus  of  one  eye  must  be  insufficient  to  keep  the 
vertical  planes  in  their  positions,  and  the  images  will  be 
apart.  Then  the  prism  placed  over  either  eye,  with  the 
base  inward,  which  will  cause  the  patient  to  see  one  line 
and  two  dots,  will  show  the  degree  of  insufficiency  of  the 
internal  rectus ;  and  with  the  base  placed  outward, 
to  produce  the  same  result,  insufficiency  of  the  external 
rectus. 

The  false  image,  or  the  one  that  is  seen  with  the 
squinting  or  deviating  eye,  is  projected  outward  or  inward 
as  the  case  may  be,  according  to  the  position  in  which  the 
rays  from  the  object  strike  upon  the  retina.  I  have  ex- 
plained to  you,  in  the  previous  part  of  this  lecture,  that. 


FIG.  61. — THE  PROJECTION  OF  THE  IMAGE  :    HOMONYMOUS  DIPLOPIA. 

when  the  image  is  above  the  macula,  the  object  will  ap- 
pear below  ;  while,  if  below  the  macula,  it  will  appear 
above.  A  similar  result  obtains  in  the  lateral  images,  as 


MUSCULAR  ASTHENOPIA. 


I29 


the  image  will  then  appear  outward  when  the  rays  fall 
upon  the  retina  inside  the  macula,  and  inward  when  they 
strike  outside  the  macula. 

In  the  above  diagram  the  object .#  is  seen  distinctly  by 
the  right  eye  £,  as  the  visual  line  Bm  passes  directly  to 
the  macula  at  m,  while  the  visual  line  of  the  other  eye 
Dm  is  turned  inward,  being  directed  toward  D ;  conse- 
quently, as  the  eye  is  turned  on  its  centre  of  rotation  y, 
the  rays  of  light  from  the  object  will  fall  upon  the  retina 
at  the  point  o,  inside  the  macula.  It  will  then  be  pro- 
jected outward  on  the  same  side  as  the  deviating  eye,  and 
the  object  will  appear  at  C,  as  shown  by  the  line  oC. 
The  distance  between  these  two  images  will  be  regulated  by 
the  degree  of  deviation  and  the  distance  at  which  the  ob- 
ject is  placed  from  the  eyes.  The  greater  the  distance  at 
which  the  object  is  placed,  the  greater  the  distance  between 
the  images,  while  the  angle  of  the  strabismus  will  remain 
the  same. 


. :_, .77 


FIG.  62. — THE  PROJECTION  OF  THE  IMAGE  :  CROSSED  DIPLOPIA. 

In  this  diagram  the  object  B  is  seen  distinctly  by  one 


130  LECTURES  ON  THE   ERRORS  OF  REFRACTION. 

eye,  but  on  the  opposite  side  from  the  deviating  eye.  We 
see  that  the  visual  line  passes  directly  from  the  object  // 
to  the  macula,  m,  of  the  right  eye,  E,  while  the  visual  line 
of  the  other  eye,  Dm,  is  deviated  to  D,  as  shown  by  the 
dotted  line,  and  consequently  is  turned  outward  on  its 
centre  of  rotation,  y.  The  rays  of  light  from  the  object 
B  fall  upon  the  retina  at  o,  outside  the  macula  m,  and  are 
projected  inward  on  the  opposite  side,  and  are  seen  at 
C,  as  shown  by  the  line  oC.  The  image  to  the  right,  C, 
is  that  of  the  left  eye  ;  and  the  image  B,  that  of  the  right 
eye. 

This  condition  is  called  crossed  diplopia,  from  the 
images  being  on  opposite  sides.  It  is  always  associated 
with  a  weakness  or  paresis  of  the  internal  rectus, 
strabismus  divergens ;  while,  if  the  image  is  seen  on  the 
same  side  as  the  deviating  eye  (fig.  6i),we  have  homony- 
mous  diplopia.  This  is  due  to  a  fault  of  the  external 
rectus,  causing  strabismus  convergens. 

The  image  that  is  formed  in  the  region  of  the  macula 
of  the  deviating  eye  in  the  direction  of  the  line  viD 
(figs.  6 1  and  62),  will  not  attract  the  patient's  attention  ; 
but  if  it  does,  it  will  not  appear  distinct.  In  most  cases 
of  squint  we  have  the  condition  of  amblyopia  ;  so  that 
the  image  formed  by  the  deviating  eye  will  not  be  dis- 
tinct, and  is  easily  suppressed. 

In  nearly  all  cases  of  squint,  unless  of  very  slight  de- 
gree, they  are  not  troubled  by  the  diplopia,  as  they  have 
learned  to  suppress  the  image  of  the  squinting  eye,  and 
monocular  vision  results. 

It  is  possible  that  you  may  have  monocular  or  uniocu- 
lar  diplopia,  a  very  rare  condition,  that  may  be  due  to 
changes  in  the  crystalline,  as  commencing  cataract,  irregu- 
lar curvature  of  the  cornea,  displacement  of  the  lens,  or 
in  cerebral  tumors,  and  should  be  examined  very  carefully. 
(NETTLES  HI  P.) 


MUSCULAR  ASTHENOPIA.  131 

These  various  tests  that  we  have  applied  to  our  patient 
will  prove  that  we  have  either  an  insufficiency  or  paresis 
of  one  or  more  of  the  ocular  muscles  ;  but  it  does  not 
show  us  which  muscle  may  be  affected,  nor  to  which  eye 
it  belongs.  We  shall  have  to  proceed  further  in  our  ex- 
amination before  we  can  decide  how  to  apply  any  correct- 
ing glass,  or  adopt  any  other  means  for  the  relief  of  the 
diplopia. 

This  brings  us  to  the  study  of  the  action  of  prisms 
upon  a  ray  of  light,  and  how  prisms  may  correct  the 
diplopia. 

You  will  remember  that  when  speaking  of  the  refrac- 
tion of  rays  of  light,  as  they  pass  through  different  media, 
we  have  found  when  passing  through  a  prism,  they  are 
bent  or  refracted  toward  the  base.  The  theory  you  will 
find  in  the  second  lecture. 

Now  the  amount  or  extent  to  which  these  rays  are  re- 
fracted will  depend  upon  the  principal  angle  of  the  prism, 
and  the  angle  of  deviation  will  be,  for  weak  prisms,  one- 
half  of  the  principal  angle.  The  prisms  that  you  find  in 
our  trial  cases  are  marked  with  numbers,  which  represent 
the  principal  angle,  and  consequently  the  angle  of  devia- 
tion will  be  one  half  of  that  number.  If  a  prism  be  marked 
20°,  this  number  will  represent  the  principal  angle  in  de- 
grees, and  the  angle  of  deviation  will  be  only  10  degrees. 
Then  the  deviation  of  the  visual  line,  when  a  diplopia  is 
corrected  by  a  prism  marked  20°,  will  represent  a  deviation 
or  squint  of  10°,  outward-  or  inward,  as  the  base  of  the 
prism  is  placed. 

By  the  angle  of  deviation,  we  mean  that  angle  which 
is  formed  with  the  line  of  incidence,  in  this  manner  : 

The  ray  of  light  passing  from  an  object  a,  strikes  the 
prism  in  its  primary  direction  at  B,  and  is  bent  toward 
the  normal,  as  shown  by  the  dotted  lines  at  the  point  of 
contact.  Crossing  the  prism  to  the  point  C,  it  now 


132 


LECTURES  ON  THE  ERRORS  OF  REFRACTION. 


emerges  in  a  direction  from  the  normal,  and  passes  to  the 
point  o.  Then,  to  cause  these  rays  to  fall  upon  the  retina 
at  the  macula,  the  eye,  placed  at  the  point  o,  must  have 
its  visual  axis  in  the  direction  of  the  line  of  emergence, 
oCt  and  the  object  will  appear  to  be  placed  at  a1.  This 
line  oCa\  with  that  of  the  line  of  incidence  AB,  when 
they  meet  at  the  point  JV,  will  form  the  angle  of  deviation 
D,  which  will  be  one  half  of  the  principal  angle  E  of  the 
prism.  Consequently,  while  the  rays  passing  through  a 
prism  will  be  bent  toward  the  base,  we  find  that  the  de- 
viation of  the  object  will  appear  toward  the  apex,  from  a 
to  a\ 


FIG.  63. — THE  ANGLE  OF  DEVIATION  AND  THE  ANGLE  OF  PRISM. 

We  will  now  proceed  to  the  practical  part  of  this  work, 
i.  e. :  How  we  shall  use  the  prism  to  measure  the  degrees 
of  squint  or  diplopia,  or  to  estimate  the  insufficiency  and 
the  power  of  the  ocular  muscles. 

In  a  case  of  diplopia,  due  to  a  paresis  or  insufficiency 
of  any  one  of  the  ocular  muscles,  you  should  first  test 
them  at  a  distance  of  20  feet,  using  the  flame  of  a  candle 
as  your  test  object.  Now  if  the  diplopia  be  constant  they 
will  see  two  flames,  placed  from  each  other,  according  to 
the  muscle  that  may  be  affected.  If  the  internal  or  ex- 
ternal rectus,  the  flames  will  be  displaced  laterally  ;  if  the 


MUSCULAR  ASTHENOPIA.  133 

superior  or  inferior  be  affected,  the  flames  will  be  dis- 
placed, one  vertically  above  the  other  ;  and  in  the  case 
of  the  oblique  muscles  you  will  find  the  flames  one  above 
the  other,  and  also  displaced  laterally ;  at  the  same  time, 
one  flame  will  be  inclined  to  one  side. 

As  regards  the  frequency  of  each  of  these  conditions, 
I  find  that,  according  to  Landolt  "  On  the  Examination  of 
the  Eyes,"  Von  Graefe  has  recorded  183  cases  of  paralysis 
of  the  muscles  of  the  eye  ;  and  that  where  the  paresis  was 
isolated,  there  were  : 

105  paralyses  of  external  rectus. 
52  of  superior  oblique. 

10  of  inferior  rectus. 

9  of  superior  rectus. 

5  of  internal  rectus. 

2  of  inferior  oblique. 

We  learn  from  these  tables  that  the  largest  number  of 
cases  of  paresis  are  the  external  rectus  and  the  superior 
oblique,  two  muscles  which  have  a  separate  and  distinct 
nervous  supply  ;  the  external  rectus,  being  controlled  by 
the  sixth  cranial  nerve  or  abducens,  and  the  superior 
oblique  by  the  fourth  cranial  nerve  or  patheticus.  All 
the  other  muscles  of  the  eye  are  controlled  by  the  impulse 
of  the  third  cranial  nerve,  the  motor  oculi.  When  an 
isolated  muscle  of  this  group  is  deficient  in  its  movements, 
it  is  due  to  a  paresis  of  one  of  the  filaments  of  this  third 
nerve,  which  supplies  the  affected  muscle. 

In  the  case  of  a  patient  who  complains  of  diplopia,  we 
will  first  place  a  disc  of  red  glass  over  one  eye,  and  then 
note  the  position  and  inclination  of  the  two  flames,  as 
seen  by  him,  one  being  colored  red  by  the  glass.  Then, 
if  they  are  displaced  laterally,  and  the  red  light  is 
seen  on  the  same  side  as  the  eye  over  which  we  have 
placed  the  red  glass,  we  have  homonymous  diplopia.  But, 
if  the  red  light  is  on  the  opposite  side,  we  have  crossed 


134  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

diplopia.  If  we  have  a  paresis  of  the  superior  or  the  inferior 
rectus,  we  will  have  the  flames  superimposed.  When  the 
superior  rectus  is  affected,  the  flame  seen  by  that  eye  will 
be  above,  and  slightly  crossed  ;  while,  if  the  inferior  rectus 
is  at  fault,  the  flame  seen  by  the  affected  eye  will  be 
below  and  slightly  crossed,  this  crossing  of  the  images 
being  caused  by  the  action  of  the  internal  rectus  muscle. 

Should  you  meet  a  case  of  complete  paralysis  of  the 
motor  oculi,  you  will  find  crossed  diplopia ;  the  eye  re- 
stricted in  its  movements,  inward,  upward,  and  downward  ; 
slight  prominence  of  the  eyeballs ;  the  upper  lid  falling ; 
the  pupils  dilated  and  immovable,  and  the  accommodation 
paralyzed, — a  condition  very  similar  to  that  of  ophthalmo- 
plegia  externa,  where  we  have  all  the  external  and  inter- 
nal muscles  of  the  eye  paralyzed,  with  the  eyeballs  very 
prominent,  from  the  loss  of  the  natural  tonicity  of  the 
recti  muscles. 

As  we  proceed  in  our  examination,  we  have  proba- 
bly decided  which  muscle  is  affected ;  but  we  will  now 
endeavor  to  locate  it,  and  find  out  the  degree  of  in- 
sufficiency. This  we  will  do  by  placing  prisms  before  one 
eye,  using  a  stronger  one  each  time,  until  the  flames  are 
brought  together  and  appear  as  one,  always  placing  the 
base  of  the  prism  over  the  muscle  that  is  affected,  and  the 
red  glass  over  the  other  eye. 

Let  us  illustrate  this  with  a  case,  in  which  we  have  a 
paresis  of  either  of  the  external  recti,  with  slight  squint 
and  homonymous  diplopia.  If  the  eye  turns  inward  on 
its  centre  of  rotation,  the  macula  must  be  carried  out- 
ward, and  consequently  the  direct  rays  from  the  can- 
dle will  fall  upon  the  retina  inside  the  macula,  and, 
being  projected  outward,  will  cause  the  images  to  be 
homonymous.  You  will  then  place  the  prism  before  one 
eye,  with  the  base  over  the  weakened  muscle  outward,  so 
that,  as  the  deviated  rays  will  be  bent  outward,  they  must 


MUSCULAR  ASTHENOPIA.  135 

fall  upon  the  macula.  When  we  have  used  a  prism  of  a 
known  degree,  and  strong  enough  in  its  refractive  power 
to  fuse  the  images  and  make  them  appear  as  one,  we  will 
have  the  degree  of  insufficiency. 

Then  when  only  one  flame  will  be  seen,  the  number  of 
the  prism,  divided  by  2,  will  give  you  the  degree  of  devi- 
ation of  the  eye  and  its  visual  line,  which  in  this  case,  if 
if  we  use  a  prism  of  20°  principal  angle,  will  show  a 
deviation  of  the  visual  line  from  the  normal  of  10°,  and 
the  angle  of  deviation  will  be  the  same  when  measured  by 
the  perimeter.  (See  figs.  56  and  60.) 


FIG.  64. — ACTION  OF  PRISM  IN  HOMONYMOUS  DIPLOPIA. 

The  theory  and  reason  for  placing  the  base  of  the 
prism  over  the  affected  muscle  are  shown  in  the  diagram. 
When  the  rays  of  light  coming  from  the  object  at  the 
point  C,  and  passing  into  both  eyes,  A  and  B,  will  in  the 
the  right  eye,  B,  fall  upon  the  macula,  m,  but  in  the  left 
eye,  A,  being  turned  inward,  with  the  visual  line  at 
Dm,  the  rays  will  fall  upon  the  retina  at  o,  a  point  inside 
the  macula,  m,  and  be  projected  outward  to  E  with 
homonymous  diplopia.  But  if  we  place  the  prism  F  over 


136  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

the  eye  A,  with  the  base  outward,  the  rays  of  light  from 
the  luminous  point,  C,  will  be  deviated  at  X  by  the  action 
of  the  prism.  When  you  have  selected  the  proper  glass, 
you  will  find  the  images  of  each  eye  fused,  when  single 
vision  results.  Then  the  degree  of  the  prism  which  will 
fuse  the  images  will  be  double  the  number  of  degrees  that 
the  eye  A  is  deviated  inward  from  the  proper  position 
when  fixed  upon  the  object  at  C. 

Should  you  find  a  weakness  of  any  of  the  other 
muscles,  you  will  proceed  to  test  them  in  the  same  man- 
ner as  we  have  tested  the  external  rectus. 

This  method  of  examination  will  show  us  that  we  have 
a  case  of  insufficiency  of  one  of  the  external  recti  muscles  ; 
or  both  may  be  affected.  Then,  to  find  out  which  indi- 
vidual muscle  is  affected  or  deficient  in  its  muscular  power, 
we  must  proceed  to  test  each  muscle  separately  in  the  fol- 
lowing manner. 

As  a  prism  bends  a  ray  of  light  toward  its  base,  then 
if  we  place  a  prism  before  the  eye  we  will  bend  the  rays 
entering  that  eye,  either  outward  or  inward,  according  to 
the  position  of  the  base.  Then,  as  the  eye  naturally  ob- 
jects to  the  diplopia  produced,  we  will,  by  the  action  of 
the  muscles,  turn  the  direction  of  the  optic  axis  either  out- 
ward or  inward,  until  the  rays  passing  in  each  eye  fall 
upon  the  macula. 

Now,  if  we  wish  to  test  the  strength  of  the  external 
rectus  muscle  individually,  to  find  what  is  the  strongest 
prism  it  can  overcome,  you  will  place  before  one  eye  a 
prism  of  a  low  degree,  say  about  2  °  or  3  °,  with  the  base  in- 
ward, as  this  will  bend  the  rays  inward  ;  the  external 
rectus  of  the  same  eye  must  turn  the  cornea  outward,  so 
as  to  cause  single  vision.  Then  the  strongest  prism  that 
can  be  placed  before  the  eye,  with  the  base  inward,  will 
show  the  power  of  that  muscle  to  turn  the  eyeball  out- 
ward. In  this  manner  we  may  test  the  relative  strength 


MUSCULAR  ASTHENOPIA.  137 

of  each  muscle,  as  represented  by  the  degrees  marked 
upon  each  glass,  taking  the  strongest  that  the  muscle  can 
overcome  and  still  have  single  vision. 


FIG.  65. — METHOD  OF  TESTING  THE  MUSCLES  WITH  PRISMS. 

Let  us  illustrate  this  with  our  diagram,  in  which  the 
rays  from  the  object  A  fall  upon  the  macula  of  each  eye 
at  m,  but,  with  a  prism  before  the  left  eye,  as  at  D,  with 
its  base  inward,  the  rays  will  be  bent  toward  E.  Then, 
to  bring  the  macula  at  E,  the  eye  B  must  rotate  on  the 
vertical  axis,  atj/,  outward.  This  action  is  produced  by 
the  external  rectus,  and  the  stronger  the  prism  the  greater 
must  be  the  efforts  of  the  muscle  to  rotate  the  eye  out- 
ward. Hence  the  strongest  prism  by  which  the  person 
examined  still  has  single  vision  will  represent  the  power 
of  the  muscle  to  act. 

In  this  test  of  the  strength  of  the  recti  muscles  you 
will  find  them  different  in  power,  according  to  the  pur- 
poses for  which  the  eyes  are  used,  viz.:  the  internal  rectus 
is  the  strongest,  next  the  external  rectus,  and  lastly  the 
superior  and  the  inferior  rectus.  The  standard  power  of 
the  internal  rectus  is  about  25  to  35  degrees  ;  i.  e.,  there 
will  be  single  vision  with  a  prism  of  that  number  of  de- 


138  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

grees,  placed  before  the  eye  with  its  base  outward.  The 
power  of  the  external  rectus  will  be  about  8  degrees,  that 
of  the  other  muscles  about  3  or  4  degrees,  the  inferior 
being  generally  the  strongest. 

If,  then,  we  have  a  case  in  which  the  action  of  the 
muscles,  when  tested  separately,  cannot  overcome  the 
deviation  of  a  prism  of  the  above  refractive  power,  we 
may  be  sure  there  is  a  deficiency  of  the  muscle  tested, 
though  there  may  be  no  diplopia  ;  but  the  muscle  power 
is  not  great  enough  to  do  the  work  required,  at  the  usual 
occupations  of  life. 

Prof.  E.  Landolt,  of  Paris,  published,  in  the  OpJitli. 
Review,  vol.  v.,  Nos.  57  and  58,  July  and  August,  1886,  a 
monograph,  translated  by  W.  T.  Law,  M.D.,  F.R.C.S., 
"  On  Insufficiency  of  the  Power  of  Convergence,"  in 
which  he  proposes  a  new  and  excellent  test  for  the  power 
of  the  internal  recti  muscles,  acting  together,  showing 
their  power  with  binocular  vision,  at  different  distances, 
by  means  of  an  instrument,  which  he  calls  the  ophthalmo- 
dynamometcr.  It  is  described  as  follows:  "This  little 
instrument  consists  of  a  cylinder  which  can  be  fixed  to 
any  candle  of  ordinary  size.  It  possesses  a  vertical  slit  of 
about  three  mm.  in  breadth,  a  vertical  line  consisting  of  a 
series  of  fine  openings,  and  a  circular  aperture  of  about 
one  mm.  in  diameter.  The  openings  are  all  covered  with 
ground  glass,  and  when  the  candle  is  lighted  they  form 
shining  objects,  thrown  into  sharp  contrast  with  the 
blackened  exterior  of  the  cylinder.  Under  each  opening 
is  placed  a  hook  to  which  can  be  attached  the  end  of  a 
measuring  tape,  constructed  to  wind  up  by  a  spring  in  the 
ordinary  way.  This  tape  is  divided  into  centimetres  on 
one  side,  beginning  from  its  free  end,  and  on  the  other 
side  into  corresponding  value  in  metre  angles  or  dioptrics, 
as  the  case  may  be. 

"  To  ascertain  the  maximum  of  convergence,  the  tape 


MUSCULAR  ASTHENOPIA. 


139 


being  partly  withdrawn,  its  case  is  held  at  the  outer  mar- 
gin of  the  orbit,  so  that  the  aperture  through  which  the 
tape  issues  is  on  a  level  with  the  point  of  rotation  of  the 
eyeball.  The  patient  is  then  told  to  look  at  the  vertical 
line  upon  the  cylinder,  and  the  instrument  is  gradually 
brought  nearer,  in  the  median  line,  until  he  says  the  line 
appears  double  (crossed  diplopia).  The  measure  is  then 
removed,  and  the  distance  of  the  punctum  proximum  read 
off  on  one  side  of  the  tape,  and  the  maximum  of  conver- 
gence upon  the  other." 

In  describing  the  use  of  this  instrument,  to  measure 
the  power  of  convergence,  we  must  take  as  a  standard  of 
i  a  metre  angle. 


FIG.  66. — DIAGRAM  SHOWING  THE  METRE  ANGLE. 

This  metre  angle  is  formed  by  the  base  line,  in  the 
above  diagram,  at  o  a,  in  passing  from  infinity  to  the 
nodal  point  of  the  eye  at  o ;  then,  if  the  eye  is  directed  to 
the  point  R,  on  the  median  line,  at  one  metre  from  the 
eye,  the  visual  line,  o  R,  with  the  base  line,  will  form  the 
angle  a  o  R,  which  will  be  one  metre  angle.  As  we 
bring  the  object  R  nearer  to  the  eyes,  in  the  median  line, 
this  angle  will  increase  in  size,  and  the  visual  axes  become 
more  and  more  converged.  Then,  according  to  Landolt, 
we  find  "  that  the  angle  of  convergence  is  in  inverse  pro- 
portion to  the  distance  between  the  eyes  and  the  fixed 
object  in  the  median  line." 

The  angle  formed  when  the  object  is  placed  at  R,  on 


140     LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

the  median  line,  is  expressed  by  R  =  ~  -=  ,)„_  or  one  unit 
of  positive  convergence  ;  then,  if  we  place  the  object  at 
one  third  metre  from  each  eye,  with  binocular  fixation, 
we  have  ^  of  £.  =  3D  or  3  metre  angles.  The  nearest 
point  of  fixation  with  both  eyes  will  give  the  greatest 
amount  of  convergence,  or  the  maximum  of  convergence  ; 
while  the  minimum  of  convergence,  in  normal  cases,  will 
be  when  the  eyes  are  perfectly  parallel,  and  represents  zero ; 
because  then  the  punctum  remotum  is  situated  at  infinity. 

This  power  of  convergence  is  called  the  positive  part, 
but  we  can  have  in  normal  eyes  a  divergence  of  the  visual 
axes  by  the  use  of  prisms  placed  before  each  eye,  with 
their  bases  inward.  This  power  of  abduction  of  the  visual 
lines  will  be  represented  as  the  negative  part  of  the  power 
of  convergence.  By  referring  to  fig.  66  this,  or  negative 
part  of  the  power  of  convergence,  is  shown  by  the  dotted 
lines  from  e  to  x. 

Now  we  require  a  certain  amount  of  this  positive 
power  of  convergence  to  perform  near  work  with  comfort 
and  without  the  symptoms  of  asthenopia.  This  should 
be  at  least  3  metre  angles  more  than  the  point  at  which 
the  work  is  required  to  be  placed.  For  instance,  if  a 
patient  reads  at  ^  of  a  metre,  or  1 2  inches  from  the  eyes, 
he  will  require  3  metre  angles  of  convergence  for  that 
distance.  But  this  is  not  sufficient  ;  he  should  have  at 
least  3  m.  a.  more  of  the  power  of  convergence  in  reserve 
to  work  comfortably  at  1 2  inches.  Consequently,  we 
should  have  a  reserve  force  twice  as  great  as  the  power  of 
convergence  employed. 

If  we  find,  then,  that  the  power  of  convergence  is  defi- 
cient, and  that  the  patient  is  suffering  from  the  effects  of 
muscular  asthenopia,  how  shall  we  treat  them  ?  First,  if 
of  low  degrees,  as  one  metre  angle,  we  may  use  prisms 
with  their  bases  outward  ;  but  we  cannot  use  very  strong 
ones,  nor  of  more  than  2  °  or  3  °  over  each  eye.  If  we  have 


MUSCULAR  ASTHENOPIA.  141 

a  greater  deficiency  of  convergence,  we  must  resort  to  sur- 
gical means,  of  which  we  may  use  tenotomy  of  the  external 
rectus.  If  this  fail,  we  must  advance  the  internal  rectus 
or  combine  both  operations,  according  to  the  desired 
result.  But  in  every  case,  before  proceeding  to  such 
extreme  measures  as  a  surgical  operation  affords,  I  would 
advise  you  to  test  the  muscles  very  carefully  several  times, 
either  by  means  of  the  prism  test  or  that  of  the  metre 
angle,  as  measured  by  Landolt's  ophthalmodynamometer. 

If  we  wish  to  order  prisms  for  the  relief  of  muscular 
asthenopia,  we  must  test  each  muscle  separately,  and  find 
the  amount  in  degrees  of  insufficiency  of  the  weakened 
muscle  ;  we  must  then  divide  this  by  2,  and  the  result 
should  be  equally  apportioned  between  both  eyes.  Thus, 
if  we  find  a  weakness  of  the  internal  rectus  of  8  degrees  ; 
by  dividing  this  by  2,  and  then  placing  one-half  of  the  result 
over  each  eye,  with  the  base  of  the  prism  over  the  weak- 
ened muscles,  we  will  have  a  prism  of  2  °  over  each  eye, 
with  their  bases  placed  inward,  and  the  strain  of  conver- 
gence will  be  relieved.  The  visual  lines  will  now  be  di- 
rected to  a  point  removed  from  the  eyes  farther  than  the 
object  is  placed. 

In  very  slight  degrees  of  insufficiency  you  may  obtain 
the  effect  of  a  very  weak  prism  by  having  the  glasses 
which  correct  the  error  of  refraction  decentred,  i.  e.,  the 
centre  of  the  glass  placed  either  outward  or  inward,  as 
needed,  so  that  the  patient  must  look  through  the  outer 
portions  of  the  glass.  All  spherical  glasses  are  the  same  as 
prisms,  with  their  bases  or  apices  together  ;  then  the  pe- 
riphery of  a  spherical  glass  must  act  as  a  prism. 

As  the  rays  of  light  proceed  from  the  point  A',  and 
pass  through  a  convex  glass  X,  with  the  centre  placed  in- 
ward, or  through  a  concave  glass  K,  with  the  centre  placed 
outward,  we  will  have  the  rays  that  would  fall  upon  the 
retina  at  d  bent  inward  to  the  macula  m,  and  the  eyes 


142 


LECTURES  ON  THE  ERRORS  OF  REFRACTION. 


will  be  directed  toward  the  point  A :  in  this  manner  we 
will  relieve  the  strain  upon  the  muscles  of  convergence. 
Consequently,  to  attain  this  object,  in  ordering  glasses, 
you  must  decentre  them,  by  placing  the  centre  of  the  con- 
vex glass  inward,  and  the  centre  of  the  concave  glass 
outward. 


FIG.  67. — ACTION  OF  DECENTRED  LENS. 

The  direction  of  the  rays  of  light,  with  their  conju- 
gate foci,  when  passing  through  the  periphery  of  a  spheri- 
cal lens,  is  shown  in  the  following  diagrams  : 


FIG.  68. — THE  PERIPHERAL  REFRACTION  OF  A  BI-CONVEX  LENS. 

The  above  diagram  represents  a  bi-convex  lens,  whose 
focal  distance  from  the  point  B  is  at  C ;  then  all  the  rays 
from  B  must  focus  at  C ;  and  if  we  take  those  passing 
through  the  periphery,  with  the  principal  ones  represented 


MUSCULAR  ASTHENOPIA. 


H3 


by  the  lines  D,  D,  we  find  that  the  rays  which  pass  through 
the  outer  portion  of  the  lens  A  are  bent  either  outward 
or  inward,  according  to  the  position  of  the  lens  to  the 
median  line  of  the  body.  The  action  of  a  concave  lens  is 
the  same  at  the  periphery,  as  shown  by  this  diagram. 


FIG.  69. — THE  PERIPHERAL  REFRACTION  OF  A  BI-CONCAVE  LENS. 

We  now  have  the  direction  of  the  rays  passing 
through  the  periphery,  shown  by  the  lines  B  D,  with  their 
respective  negative  foci  represented  by  the  dotted  lines. 
The  lines  in  the  two  last  diagrams  will  be  the  central  ray 
of  that  portion  of  the  convex  or  concave  lenses. 

You  will  find  this  method  of  -decentring  the  glasses 
very  useful  in  some  cases,  and  it  should,  if  possible,  be  pre- 
ferred to  that  of  adding  prisms,  as  it  will  make  the  glasses 
so  much  lighter  and  thinner  ;  but  it  can  only  be  used  in 
cases  where  the  weakness  of  the  muscle  is  very  slight. 


EIGHTH    LECTURE. 

ASTIGMATISM. 

History — First  cases  recorded — The  triaxial  ellipsoid — Division  or  varieties — Irregu- 
lar astigmatism — Causes — Symptoms — Correction — Diagnosis — The   keratoscope 
— Placido's  method  of  diagnosis — Regular  astigmatism — Refraction  of  a  spherical 
and  a  cylindrical  lens  combined — The  two  focal  points — "  Interval  of  Sturm  "- 
Position  of  retina — Astigmatism   depends  on   curvature   of   the  cornea — Simple 
hypermetropic — Simple   myopic — Compound    hypermetropic — Compound  myopic 
— Mixed  astigmatism — Direction  of  the  two  principal  meridians — Direction  ot 
in  simple — In  compound — In  mixed — Concealed — Landolt  on — Method  of  testing 
for — Green's  card  test — Javel's  card  test — The  stenopaeic  slit — Diagnosis  with  the 
ophthalmoscope. 

GENTLEMEN  : — We  have  been  considering  the  eyeball 
in  refraction,  according  to  the  length  of  the  optic  axis, 
finding,  that  it  was  too  short  in  hypermetropia,  and  too 
long  in  myopia,  while  the  chief  refraction  surface,  the 
cornea,  has  been  taken  as  a  perfect  surface  of  revolu- 
tion, it  being  equal  in  all  its  different  meridians,  as  far 
as  its  refractive  power  was  concerned,  and  that  all  rays  of 
light  passing  inward  would  come  to  a  focus  at  some  point 
on  the  visual  axis.  But  we  may  have  a  different  surface 
than  that  of  the  normal  cornea,  in  which  rays  of  light 
coming  from  infinity,  and  being  parallel,  will  be  refracted 
more  or  less  in  one  meridian  than  the  other  according  to 
the  curvature  of  the  cornea  in  each  meridian. 

This  condition  is  called  astigmatism,  and  generally 
has  its  seat  in  the  curvature  of  the  cornea,  though  it  may 
exist  in  the  surfaces  of  the  lens.  I  think,  if  we  consider 
that  all  cases  of  astigmatism  are  due  to  an  unequal  re- 
fraction of  different  meridians  of  the  corneal  surface,  it 

144 


A  S TJGMA  TISM.  1 45. 

will  assist  us  very  much  in  the  study  of  this  interesting 
division  of  ametropia. 

It  is  a  curious  fact  that  the  first  recorded  case  of 
astigmatism,  that  of  Thomas  Young,  in  1801,  was  due 
to  changes  in  the  curvature  of  the  lens,  in  speaking  of 
which  he  says  :  "  His  eye  in  the  state  of  relaxation  col- 
lects to  a  focus  on  the  retina  those  rays  which  diverge 
vertically  from  an  object  at  the  distance  of  ten  inches 
from  the  cornea,  and  the  rays  which  diverge  horizontally 
from  an  object  at  seven  inches  distance."  So  that  the  rays 
in  the  vertical  meridian  must  have  been  focused  on  the 
retina,  just  as  in  an  eye  that  is  myopic  of  one-tenth,  and 
in  the  horizontal  meridian  myopic  one-seventh. 

The  next  case,  that  of  MR.  AIRY,  reported  in  1827, 
was  also  a  case  of  compound  myopic  astigmatism,  in 
which  he  proved  that  the  cornea  was  not  a  perfect  surface 
of  revolution,  but  that  the  curvature  was  greater  in  the 
vertical  meridian  than  in  the  horizontal,  and  that  in  both 
meridians  it  was  more  convex  than  in  the  normal  or  em- 
metropic  eye.  But  it  was  not  generally  known  until 
Donders  completed  his  investigations,  and  gave  us  the 
correct  views  on  the  nature  and  the  causes  of  astigmatism. 

This  condition  generally  exists  in  all  normal  eyes,  but 
only  to  a  very  slight  degree,  less  than  ^,  and  conse- 
quently does  not  disturb  the  vision  sufficiently  to  call  for 
any  correction  by  glasses.  When  it  becomes  noticeably 
greater  than  that  amount  it  will  require  proper  considera- 
tion at  your  hands,  though  I  would  advise  you  to  correct 
even  the  smallest  degree  of  astigmatism  if  it  causes  any 
symptoms  of  asthenopia. 

If  we  find  that  the  curvature  of  the  cornea  is  different 
in  any  two  meridians,  at  right  angles  to  each  other,  its 
surface  will  not  present  that  of  a  perfect  surface  of  revo- 
lution, but  that  of  a  triaxial  ellipsoid,  in  which  we  find 
three  distinct  axes — first,  of  the  central  axis,  on  the  visual 


146  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

line  ;  then  of  the  vertical ;  and  lastly,  of  the  horizontal 
meridian.  These  two  last  axes  may  be  shorter  or  longer 
than  each  other,  according  to  the  degree  of  refraction,— 
being  longer  than  normal  in  a  case  of  hypermetropia,  and 
shorter  than  normal,  with  a  corresponding  greater  curve, 
in  myopia. 

The  word  astigmatism,  as  applied  to  refraction,  signifies 
that  rays  of  light  from  a  point  are  not  reunited  at  a  point ; 
or  that  the  rays  in  the  different  meridians  will  focus  at 
different  points  on  the  visual  axis  as  a  line.  We  will 
first  divide  astigmatism  into  two  forms,  REGULAR  and 
IRREGULAR.  The  last  variety  I  shall  consider  very 
briefly,  because  it  offers  so  few  means  for  its  relief. 

In  irregular  astigmatism  we  may  not  only  have  a 
difference  in  the  curvative  of  the  meridians,  but  a  differ- 
ence in  the  curvature  of  a  single  meridian,  generally  caused 
by  some  disease  of  the  cornea.  This  will  leave  its  surface 
irregular  in  certain  parts ;  as  in  the  healing  process  of 
ulceration,  the  outer  surface  of  the  cornea  has  small  facets 
which  will  materially  interfere  with  the  refraction  of 
parallel  rays  of  light  in  that  meridian.  We  have  it  also  in 
conical  cornea,  and  in  that  condition  of  the  crystalline  lens 
in  which  the  refraction  of  the  various  sections  is  different. 

This  condition  of  irregularity  is  very  annoying  to  the 
individual,  as  he  will  see  all  objects  in  a  blurred  condition, 
distorted  and  irregular  in  all  their  parts.  Our  means  for 
its  relief  are  limited,  as  it  is  very  obvious  that  this  condi- 
tion cannot  be  corrected  by  glasses.  We  must  cut  off  all 
the  peripheral  rays,  and  allow  the  light  to  pass  through 
only  a  small  portion  of  the  cornea.  This  can  be  done  by 
means  of  an  opaque  diaphragm,  with  a  small  hole  in  the 
centre  about  i  or  2  mm.  in  diameter,  held  close  to  the 
eye,  in  the  position  that  will  give  the  best  vision,  the 
aperture  being  placed  over  that  portion  of  the  cornea 
•which  has  the  most  regular  refraction, 


A  S  TIG  MA  TISM.  1 47 

You  will  readily  see  that,  though  by  this  means  we 
shut  off  a  large  portion  of  the  rays  of  light  proceeding 
from  an  object  and  reduce  the  illumination,  we  at  least 
gain  the  advantage  of  a  perfect  focus  for  those  few  rays 
which  pass  through  the  opening  in  the  centre. 

You  will  be  surprised  how  much  the  sight  of  some  of 
these  individuals  will  be  improved  by  this  means.  I  can 
at  present  recall  a  case  in  my  practice  of  a  patient  who 
was  almost  blind,  unable  to  distinguish  any  object  clearly, 
and  yet  with  a  small  opening  in  a  diaphragm  of  metal 
could  readily  distinguish  the  figures  on  the  face  of  a  small 
watch.  This  disc  must  be  as  close  to  the  eye  as  possible, 
as  the  farther  it  is  removed  the  smaller  will  be  the  field  of 
vision. 

A  most  interesting  experiment,  which  will  show  you  the 
difference  of  refraction  in  different  parts  of  the  meridians, 
even  of  the  normal  eye,  is  to  hold  the  thumb  and  fore- 
finger between  one  eye  and  a  light  shaded  with  a  white 
opaque  globe.  You  will  then  notice  that,  as  the  fingers 
are  brought  nearer  each  other  the  outlines  are  very  indis- 
tinct, and  as  they  touch  each  other  it  will  appear  as  if  a 
small  drop  of  a  dark  liquid  lay  between.  Now  place 
before  the  eye  a  card-board  with  a  small  pin-hole  through 
it,  and  looking  through  this  opening  you  will  cut  off  all 
the  rays  of  light  that  pass  through  the  periphery  of  the 
cornea,  the  drop  disappears,  and  the  edges  of  the  fingers 
are  well  defined.  It  is  this  curvature  that  causes  the  stars 
and  other  lights  at  night  to  have  their  radii,  which  would 
disappear  if  the  curvature  of  a  cornea  were  perfect. 

The  most  ready  means  for  the  diagnosis  of  irregular 
astigmatism  is  that  of  the  ophthalmoscope.  By  illumina- 
tion of  the  eye  at  a  distance  of  ten  or  twelve  inches,  you 
will  notice  that  the  reflex  from  the  fundus  is  not  clear 
in  all  its  parts,  but  that  certain  portions  of  it  will  be 
cut  off  and  appear  as  dark  spots  on  the  cornea.  This  is 


148  LECTURES   ON  THE  ERRORS  OF  REFRACTION. 

caused  by  the  return  rays  of  light,  as  they  are  reflected 
from  the  retina,  being  refracted  in  such  a  direction  that 
they  cannot  enter  the  eye  of  the  observer.  Conical  cornea 
is  well  illustrated  by  this  means,  as  it  will  appear  as  dark 
rings  inside  of  the  periphery  of  the  cornea,  changing 
their  position  and  shape  as  the  light  is  moved.  In  the 
examination  of  the  fundus  you  will  find  that,  although  the 
eye  can  be  illuminated,  the  vessels  and  disc  will  appear  dis- 
torted and  indistinct  in  certain  parts. 

PLACIDO,  of  Porto,  has  devised  a  very  interesting  method 


6ga. — PLACIDO'S  KERATOSCOPE. 

for  the  diagnosis  of  astigmatism,  both  regular  and  irregular, 
in  which  he  uses  a  disc  of  card-board  or  zinc,  about  23 
centimetres  in  diameter,  with  a  central  aperture  of  about  i 
centimetre  ;  to  which  is  attached  a  small  tube  about  3 
centimetres  long.  On  the  opposite  side  is  painted  a 
series  of  concentric  circles,  alternately  black  and  white. 
This  instrument  PLACIDO  calls  the  kcratoscopc.  To  use  it, 
we  place  the  patient  with  his  back  toward  a  window,  and 
then  with  the  disc  reflect  the  light  from  a  window  to  the 
eye  to  be  examined,  when  we  will  see  the  image  of  those 
circles  on  the  cornea  by  looking  through  the  central  aper- 


A  S  TIGMA  TISM.  1 49 

ture.  If  the  curvature  of  the  cornea  be  normal,  we  will 
see  the  circles  in  their  regular  shape  ;  but  if  there  be  reguj 
lar  astigmatism  the  image  will  appear  oval,  with  the  long- 
est diameter  in  the  meridian  nearest  to  the  normal  curve  ; 
while  if  the  cornea  be  the  seat  of  irregular  astigmatism, 
the  image  will  appear  very  much  distorted  and  some  por- 
tions of  the  circles  will  not  be  seen. 

In  regular  astigmatism  we  study  the  different  meridi- 
ans and  their  planes,  each  one  separate  from  the  other, 
but  it  will  only  be  necessary  for  us  to  consider  the  two 
principal  meridians.  The  intermediate  ones  have  no 
focal  points,  consequently  we  can  leave  them  out  in  all 
our  calculations.  Taking,  then,  these  two  principal  meridi- 
ans, with  their  planes,  we  shall  find  them  always  at  right 
angles  to  each  other  and  with  their  ^respective  anterior  and 
posterior  focal  points. 

Before  we  enter  on  the  study  of  these  meridians  and 
their  planes,  let  us  consider  the  action  and  direction  of 
rays,  as  they  pass  through  a  refractive  medium,  the  same  as 
that  of  an  astigmatic  eye,  and  then  we  can  better  appreci- 
ate the  refraction  of  astigmatism.  To  do  this  we  require 
a  convex  spherical  lens  to  represent  the  refraction  of  an 
emmetropic  eye  ;  a  convex  cylindric  lens  to  represent  the 
astigmatism  ;  a  point  of  light ;  with  a  screen  to  represent 
the  retina.  Now,  you  will  remember  that  the  focal  point 
of  a  spherical  lens  is  round,  and  situated  at  its  focal  distance, 
according  to  the  curvature  of  the  surfaces  ;  also  that  the 
focal  point  of  a  cylindrical  lens  forms  a  line  the  same 
length  as  its  diameter,  and  for  parallel  rays  always  found 
at  the  focal  distance  of  its  curved  surface,  parallel  to  the 
axis. 

If  we  place  these  two  lenses  together,  and  pass  the 
rays  of  light  through  them,  you  will  find  that  we  have 
two  focal  points,  each  represented  by  a  short  focal  line. 
The  first  focal  line  is  situated  at  the  focal  distance,  which 


I5O      LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

is  found  by  the  addition  of  the  focal  power  of  the  two 
lenses  combined  ;  and  the  second,  at  the  focal  distance  of 
the  spherical  lens  alone.  These  two  focal  lines  will  be 
found  on  the  principal  axis  of  the  combined  lenses.  This 
can  be  easily  shown  by  placing  the  screen  at  a  suitable  dis- 
tance from  the  lenses,  and  your  point  of  light  at  infinity. 
At  all  other  points  there  will  be  no  distinct  images,  but 
only  an  illuminated  portion  of  different  shapes,  formed  by 
the  circles  of  diffusion,  as  the  rays  pass  between  or  beyond 
the  focal  points.  The  interval  or  space  between  these 
two  focal  points,  or  focal  lines,  is  called  the  "  interval  of 
STURM,"  and  we  will  find  the  direction  of  the  lines  form- 
ing these  two  focal  points, — one  parallel  with,  the  other  at 
right  angles  to,  the  axis  of  the  cylindrical  glass. 

Let  us  place  a  convex  cylindric  glass  of  -fa  focal  dis- 
tance over  a  convex  spherical  lens  of  j1^,  with  the  axis 
vertical.  Then  all  the  rays  that  pass  through  the  lenses, 
in  the  same  plane  as  the  axis  of  the  cylindric  lens,  would 
be  only  focused  by  the  spherical  lens,  at  a  point  ten 
inches  from  the  combined  lenses  ;  while  all  the  rays  that 
would  pass  in  a  plane  at  right  angles  to  the  axis  would  be 
refracted  by  the  power  of  both  lenses,  and  would  form  a 
distinct  line  at  five  inches  from  them. 

But  why  do  these  focal  points  form  lines  by  this  com- 
bined system  of  lenses  ? 

To  explain  this  I  must  refer  you  to  figs.  70  and  71. 
In  the  vertical  plane  we  will  represent  the  refraction  of 
the  rays  as  they  pass  through  the  combined  lenses  in  a 
plane  parallel  with  the  axis  of  the  cylindric  glass.  In 
this  plane  the  cylindric  lens  does  not  bend  the  rays, 
which  are  only  refracted  by  the  spherical  lens.  But  in  the 
opposite  meridian  or  plane,  at  right  angles  to  this  (see 
fig.  71),  we  have  the  rays  refracted  by  both  lenses,  and 
the  focus  is  at  a  much  nearer  point. 

If  we  take  the  first  focal  distance  or  line  in  the  two 


A  S  TIGMA  TISM.  1 5 1 

planes  at  right  angles  to  each  other,  which  we  find  at  a 
(fig.  71),  then  all  the  rays  that  pass  in  the  horizontal 
plane  will  focus  at  the  point  a  on  the  principal  axis  oo. 
But  we  find  that  the  rays  passing  in  the  vertical  plane, 
parallel  with  the  axis  of  the  cylindric  glass,  have  not  yet 
come  to  their  focal  point,  and  will  fall  upon  the  screen 
at  the  point  a  as  a  vertical  line  cb  (fig.  70),  whose  length 
would  be  from  b  to  c.  As  we  now  remove  the  screen 
from  the  lenses,  all  distinct  focus  is  replaced  by  circles  of 
diffusion.  These  form  an  ellipse,  with  the  long  axis  ver- 


FIG.  70. — VERTICAL  PLANE,  COMPOUND  CYLINDRIC  LENS. 


FIG.  71. — HORIZONTAL  PLANE,  COMPOUND  CYLINDRIC  LENS. 

tical,  until  the  screen  is  a  little  less  than  midway  between 
the  focal  points,  when  the  diffusion  circles  become  round 
at  o'o'  and  o'o'  (both  diagrams).  Removing  the  screen 
still  farther,  we  have  the  same  blurred  ellipse,  but  now 
with  its  long  diameter  horizontal,  until  we  reach  the  sec- 
ond focal  point,  at  d  (fig.  70),  when  we  have  a  distinct 
horizontal  line.  This  is  formed  by  the  focus  of  the  rays 
in  the  vertical  plane,  and  drawn  outward  as  a  line  by  the 
diverging  of  the  rays  of  light  which  have  already  focused 
at  the  point  a,  in  the  horizontal  plane  (see  fig.  71),  repre- 
sented by  the  line  e  to  f. 


152 


LECTURES  ON  THE   ERRORS  OF  REFRACTION. 


We  have  then  two  focal  points,  formed  first  by  the 
rays  of  one  plane  being  brought  to  a  focus,  and  by  the  rays 
of  the  opposite  plane  before  they  have  reached  the  focal 
point  ;  and  second,  the  focal  point  of  the  vertical  plane, 
and  the  divergent  rays  of  the  horizontal  plane.  You  will 
notice  that  these  lines  are  formed  by  the  rays  which  are 
not  in  focus,  and  the  edges  of  the  lines  by  the  rays  which 
are  in  focus,  as  you  trace  the  course  of  the  rays  to  each 
focal  point. 


FIG.   72. — COMPOUND   CYLINDRIC  LENS,  ILLUSTRATING   ASTIGMATISM. 
(VERTICAL  PLANE.) 


FIG.  73. — COMPOUND  CYLINDRIC  LENS,  ILLUSTRATING  ASTIGMATISM. 
(HORIZONTAL  PLANE.) 

If  we  now  replace  the  combined  lenses  by  the  dioptric 
apparatus  of  the  human  eye,  and  the  screen  by  the  retina, 
you  will  see  that  different  positions  of  the  retina  on  the 
optic  axis  must  influence  the  direction  of  the  rays  as  they 
strike  the  retina,  and  there  produce  all  the  different  forms 
of  refraction.  If  we  place  the  retina  at  the  position  of 
the  line  aa  and  a'a'  (figs.  72  and  73)  on  the  principal 
axis,  the  rays  will  fall  upon  it  in  both  meridians  or  planes, 
the  same  as  in  the  hypermetropic  eye,  before  a  focal  point 
is  reached,  but  more  separated  in  one  meridian  than  in  the 


A  S  TIG  MA  TISM.  \  5  3 

other  (compound  hypermetropic  astigmatism).  At  the  posi- 
tion of  the  line  bb  and  b'  the  focus  of  one  meridian  is  at 
the  focal  point,  b'  (emmetropic)  ;  the  other  still  hyper- 
metropic, bb  (simple  hypermetropic  astigmatism).  At  the 
position  of  the  line  cc  and  -c  c'  one  meridian  is  still 
hypermetropic,  cc ;  but  the  rays  in  the  other  have  now 
met  in  front  of  the  retina,  and  therefore  at  c'c'  this 
meridian  is  myopic  (mixed  astigmatism).  The  retina  is 
beyond  the  focal  distance  of  the  second  meridian.  At 
the  position  of  the  line  df.and  d'd'  the  rays  of  the  verti- 
cal meridian  have  now  come  to  the  focal  point,  d  (emme- 
tropic) ;  but  the  horizontal  meridian  is  still  myopic,  d'd' 
(simple  myopic  astigmatism)  ;  and  then,  if  the  retina  be 
placed  still  farther  away  from  the  refractive  apparatus,  as 
in  the  position  of  the  line  ee  and  e'e',  the  rays  in  both 
meridians  will  strike  the  retina  after  they  have  passed 
the  focal  points,  and  both  meridians  will  be  myopic,  but 
more  in  one  meridian  than  in  the  other  (compound 
myopic  astigmatism). 

The  distance  between  the  two  focal,  points,  as  from  a 
to  d  (figs.  70  and  71),  or  b'  to  d  (figs.  72  and  73),  will 
represent  the  focal  interval  of  Sturm,  consisting  of  the 
various  changes  in  the  circles  of  diffusion,  as  the  screen 
recedes  from  the  anterior  to  the  posterior  focal  plane. 

Let  us  now  apply  these  principles  to  the  astigmatic 
eye  and  its  different  conditions  of  refraction. 

We  have  stated  that,  as  a  rule,  all  cases  of  astigmatism 
depend  upon  the  greater  or  less  curvature  of  certain 
meridians  of  the  corneal  surface,  different  from  that  of 
the  normal  surface  of  revolution.  As  this  curvature  is 
greater  or  less,  just  so  much  will  we  have  more  or  less 
refractive  power  in  their  respective  meridians.  We  may 
have  the  curvature  of  one  meridian  normal ;  consequently 
the  rays  passing  inward  in  that  plane  will  focus  upon  the 
retina,  while  the  meridian  at  right  angles  to  it  may  be 


154  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

more  or  less  convex,  so  that  the  rays  in  this  plane  will  be 
focused  either  before  or  behind  the  retina,  according  to 
the  refractive  power  of  the  meridian  of  the  cornea. 

Astigmatism  is  divided  into  five  varieties,  according  to 
the  curvature  of  the  two  principal  meridians  of  the  cornea, 
as  follows : 

First — Simple  hypermetropic  astigmatism  (Ah.),  in 
which  the  curvature  of  one  meridian  is  normal  and  the 
rays  passing  inward  in  that  plane  will  focus  upon  the 
retina ;  while  in  the  meridian  at  right  angles  to  this  the 
curvature  is  less  than  normal,  and  consequently  the  rays 
passing  inward  in  this  plane  will  focus  behind  the  retina. 

Second — Simple  myopic  astigmatism  (Am.),  in  which 
the  refraction  in  one  meridian  is  normal,  while  that  in  the 
other  is  myopic,  or  will  focus  the  rays  in  front  of  the 
retina. 

Third — Compound  hypermetropic  astigmatism  (H. 
with  Ah.),  in  which  both  meridians  are  hypermetropic, 
but  one  more  than  the  other ;  or  the  refraction  of  the  eye 
is  hypermetropic — i.  e.,  the  optic  axis  is  shortened,  while 
the  curvature  of  the  cornea  is  the  same  as  that  in  simple 
hypermetropic  astigmatism. 

Fourth — Compound  myopic  astigmatism  (M.  with 
Am.),  in  which  both  meridians  are  myopic,  but  one  of  a 
greater  degree  than  the  other  ;  or  the  refraction  of  the  eye 
is  myopic — that  is,  the  optic  axis  is  too  long,  while  the 
curvature  of  the  cornea  is  the  same  as  that  in  simple 
myopic  astigmatism. 

Fifth — Mixed  astigmatism  (Ahm.,or  Amh.,  according 
to  the  predominating  degree  of  refraction),  in  which  one 
meridian  is  hypermetropic,  and  the  other  myopic,  at  right 
angles  to  each  other. 

You  will  then  understand  that  we  only  consider  the 
two  principal  meridians  and  their  refraction  in  each  plane, 
calculating  the  refraction  both  with  the  test  glasses, 


^  S  TIG  MA  TISM.  I  5  5 

retinoscopy  and  the  ophthalmoscope,  each  one  separately, 
and  without  regard  to  the  refraction  of  the  intermediate 
meridians. 

Landolt  gives  us  the  following  definition  of  astigma- 
tism :  "  Regular  astigmatism  is  that  condition  in  which 
the  refraction  is  different  in  the  different  meridians  of  the 
eye."  This,  then,  will  cause  the  cornea  to  have  that  form 
of  a  triaxial  ellipsoid,  with  the  two  principal  meridians 
generally  vertical  and  horizontal,  the  greatest  curve  being 
in  the  vertical  meridian  ;  but  the  principal  meridian  may 
be  inclined  from  the  vertical,  and  occupy  the  position  of 
any  of  the  degrees  of  the  arc  of  a  circle  from  o°  to  180°. 
(See  fig.  22.) 

A  peculiar  fact  connected  with  this  is,  that  you  will 
generally  find  the  principal  meridians  to  correspond  in  each 
eye,  viz.  :  If  one  meridian,  say  of  the  right  eye,  incline 
toward  the  nose  at  an  angle  of  45  °  from  the  vertical,  you 
will  also  have  the  corresponding-meridian  of  the  other  eye, 
the  left,  inclined  toward  the  nose  at  an  angle  of  135  °,  being 
45  °  degrees  on  the  opposite  side  of  the  vertical.  Also  if 
one  meridian  incline  toward  the  temple,  the  meridian  of 
the  other  eye  will  incline  that  way.  Finally,  you  may  have 
some  cases,  in  which  one  meridian  will  incline  toward  the 
nose  and  the  other  toward  the  temple,  both  being  situ- 
ated at  the  same  degree. 

Let  us  now  follow  the  course  of  the  rays  of  light  as 
they  pass  through  the  dioptric  media,  in  the  two  principal 
planes  of  the  astigmatic  eye,  in  each  of  the  several  varie- 
ties. First,  we  take  the  two  principal  meridians  of  the  eye 
in  simple  hypermetropic  and  simple  myopic  astigmatism, 
as  shown  in  the  diagram  facing  page  155. 

We  will  take  the  rays  of  one  meridian,  say  the  vertical, 
and  represent  the  refraction  and  focus  by  the  lines,  while 
in  the  planes  at  right  angles  to  that,  we  will  represent  the 
refraction  and  focus  by  the  red  dotted  lines  (- )  in 


156  LECTURES  ON  THE  ERRORS  Qf  REFRACTION. 

hypermetropia,  and  by  the  green  lines  and  dots  ( 

-)  in  myopia. 

Now  the  retina  being  situated  at  a,  all  the  rays  passing 
in  the  vertical  plane,  with  the  normal  curve  of  the  cornea 
a',  will  focus  on  the  retina  at  a.  But  in  the  case  of  hyper- 
metropia, the  curvature  of  the  cornea,  b',  in  this  mrri- 
dian,  being  less  than  normal,  the  rays,  as  shown  by  the 
dotted  lines,  will  focus  behind  the  retina,  at  6,  on  the  vis- 
ual axis  oo.  They  will  strike  upon  the  retina,  at  x  .r, 
before  they  have  come  to  a  focus,  and  will  there  form  a 
line  parallel  with  the  hypermetropic  meridian. 

The  same  result  takes  place  in  the  myopic  meridian, 
as  shown  by  the  lines  and  dots ;  as, — the  emmetropic 
meridian  being  shown  by  the  lines. — The  rays  in  the 
myopic  plane,  refracted  by  the  increased  curvature  of  the 
cornea  at  c',  will  come  to  a  focus  at  c,  before  they  have 
reached  the  retina ;  there  crossing  at  the  focal  point,  on 
the  visual  axis  oo,  they  will  strike  the  retina  in  a  divergent 
direction,  at  x  x,  and  form  a  line  in  the  same  meridian  as 
that  of  the  increased  curvature. 

If  we  now  pass  to  the  compound  forms  of  astigmatism, 
as  shown  in  the  diagram  facing  page  1 56,  the  position  of  the 
retina,  a"  is  now  changed  :  in  hyperopia,  being  in  front  at 
b",  and  in  myopia,  behind  at  c".  Consequently,  if  we  repre- 
sent the  vertical  meridian  by  the  black  lines,  we  will  see  that 
in  the  case  of  hypermetropia,  with  the  retina  at  b",  the  rays 
in  a  vertical  meridian  will  focus  behind  the  retina  at  a. 
The  rays  in  the  opposite  or  horizontal  meridian — as  shown 
by  the  red  dotted  line — will  focus  still  farther  at  a  point 
behind  the  retina,  at  6,  so  that  the  image  upon  the  retina 
will  be  blurred  in  both  meridians,  the  rays  in  the  vertical 
plane  being  refracted  by  the  normal  curvature  of  the  cor- 
nea a',  and  the  horizontal  plane  by  the  hyperopic  cur- 
vature 6'.  Again,  the  same  combination  takes  place  in 
compound  myopic  astigmatism, — as  shown  by  the  green 


o — 


A  S  TIGMA  TISM.  157 

lines  and  dots,  in  the  horizontal  meridian,  and  by  the  black 
lines  in  the  vertical  meridian.  But  in  this  case  the  retina  is 
situated  at  c",  behind  its  normal  position,  the  optic  axis 
being  elongated.  Consequently  the  rays  of  light  of  the 
vertical  and  horizontal  meridians  will  both  focus  at  points 
in  front  of  the  retina  and,  crossing,  will  form  blurred 
images, — one  focal  point  being  at  c,  and  the  other  at 
a,  both  in  front  of  the  retina  at  c"  ;  the  rays  in  the  vertical 
plane  being  refracted  by  the  curvature  of  the  cornea  a', 
and  those  in  the  horizontal  plane  by  the  myopic  curve  at  c'. 

As  we  take  the  last  variety  in  the  diagram  facing  page 
157,  that  of  mixed  astigmatism,  we  again  find  the  retina  at  its 
normal  position  a,  but  owing  to  the  curvature  of  the  cornea 
the  rays  in  both  principal  meridians  or  planes  will  not  focus 
on  the  retina.  In  one  meridian  they  will  focus  in  front  of  the 
retina  (myopic),  and  one  behind  the  retina  (hyperopic). 
If  we  illustrate  the  vertical,  hyperopic  meridian  by  the 
red  dotted  line,  and  the  curve  b'  of  the  cornea,  we  find 
that  the  rays  in  this  meridian  will  focus  behind  the  retina. 
The  horizontal,  myopic  meridian — shown  by  the  green 
lines  and  dots,  and  the  curve  c'  of  the  cornea — will  focus 
in  front  of  the  retina  at  c.  No  distinct  image  can  then 
be  formed  at  the  retinal  plane,  when  the  convergent  rays 
o  o,  and  the  divergent  rays  x  x,  fall  upon  it,  as  one  focal 
point  will  be  at  c,  and  the  other  at  b.  Now  these  several 
varieties  of  astigmatism  must  then  depend  ypon  two 
principal  facts  :  first,  the  changes  in  the  curvature  of  the 
cornea  at  certain  meridians  ;  second,  the  length  of  the 
optic  axis  affecting  the  focus  of  the  rays  in  all  meridians  ; 
and,  last,  that  in  mixed  astigmatism  we  have  a  decided 
change  from  the  normal  curvature  of  the  cornea  in  both 
principal  meridians,  making  one  myopic  and  the  other 
hyperopic. 

I  think  that  this  method  of  explaining  the  various 
forms  of  astigmatism  is  the  most  simple  and  easy  to  un- 


158      LECTURES  ON  THE  ERRORS  Oh'  REFRACT1OX. 

derstand,  leaving  out  of  our  consideration  those  rare 
cases  in  which  the  astigmatism  is  due  to  changes  in  the 
curvature  of  the  lens  surfaces.  Their  diagnosis  is  too 
complex  for  the  scope  of  these  lectures,  while  their  cor- 
rection by  cylindric  glasses  is  the  same. 

Let  me  caution  you  at  this  point  that  you  may  meet 
cases  of  astigmatism  that  will  be  concealed  or  caused 
by  an  irregular  contraction  of  the  ciliary  muscle,  thus 
changing  the  refraction  of  the  lens  in  different  meridians. 
This  condition  you  will  discover  by  the  action  of  atropine, 
and  by  the  ophthalmoscope.  If  concealed,  the  action  of 
atropine  on  the  ciliary  muscle  will  cause  the  astigmatism 
to  become  apparent  with  the  trial  by  glasses.  Landolt, 
in  his  work  on  Refraction,  page  322,  calls  this  condition 
of  unequal  contraction  of  the  ciliary  muscles  "  dynamic 
astigmatism  of  the  crystalline,"  and,  where  the  lens  causes 
the  astigmatism  when  in  a  passive  state,  "  static  astigma- 
tism of  the  crystalline."  But,  preceding  that,  Landolt 
says,  on  the  same  page  :  "In  the  vast  majority  of  cases, 
fortunately,  it  suffices  to  know  the  total  astigmatism  of  the 
eye,  without  our  needing  to  concern  ourselves  with  the 
question  as  to  what  part  is  due  to  the  cornea  and  how 
much  to  the  crystalline." 

Let  us  now  determine  the  amount  or  degree  of  astig- 
matism present  in  a  given  case,  and  consider  the  methods 
which  we  shall  use  for  obtaining  that  result. 

In  all  cases  our  first  test  must  be  with  the  trial  glasses, 
using  those  which  are  spherical  to  correct  any  condition  of 
hypermetropia  or  myopia  that  may  be  present,  proceeding 
the  same  as  we  would  in  the  examination  of  simple  cases 
of  ametropia  without  astigmatism.  We  then  select  the 
strongest  glass  that  the  patient  will  accept  in  hyperme- 
tropia, and  the  weakest  glass  in  myopia.  With  these 
glasses  properly  selected,  in  astigmatism  we  find  that  the 
-acuteness  of  vision  does  not  correspond  to  the  normal 


A  S  TIGMA  7  'ISM.  I  5  9 

vision  of  -|-§- ;  or  that  the  patient  will  miscall  certain  letters 
on  one  line,  while  he  may  see  similar  letters  on  another 
line — as,  for  instance,  he  may  see  with  a  convex  or  concave 
glass,  as  the  case  may  be,  -§-§-  or  perhaps  -f-2-. 

Now  to  commence  our  examination,  we  would  select 
the  strongest  convex  glass  that  will  give  the  best  vision  at 
twenty  feet.  Then  I  prefer  to  take  a  convex  glass  about 
,05  D  weaker  than  this,  place  it  before  the  examined  eye, 
and  add  to  it  a  cylindric  glass.  First,  with  the  axis  at 
1 80°  or  horizontal,  and  slowly  rotating  the  axis  from  right 
to  left,  find  the  meridian  at  which  the  vision  is  improved. 
At  this  meridian  place  the  strongest  convex  cylindric 
glass  which  will  give  the  best  vision  for  the  letters 
placed  at  infinity  or  twenty  feet.  If  this  combination  of 
a  spherical  and  a  cylindric  glass  cause  the  vision  to 
equal  J-j}-,  we  then  have  a  case  of  compound  hyperme- 
tropic  astigmatism. 

But  if  we  find  no  improvement  with  the  convex  cylin- 
dric glass,  we  may  then  try  a  concave  cylindric  over  a 
convex  spherical,  always  commencing  with  a  glass  having 
the  same  refractive  angle,  only  negative,  as  the  convex 
spherical  already  placed  before  the  eye.  Placing  this 
concave  cylindric  glass  with  its  axis  at  180°,  turn  the  axis 
slowly  to  the  left,  and,  if  it  give  perfect  vision  (|-§-)  at 
any  meridian,  you  will  then  have  a  case  of  simple  hyper- 
metropic  astigmatism.  You  can  prove  this  by  removing 
both  glasses  and  substituting  a  convex  cylindric  glass  of 
the  same  refractive  power.  For  instance,  if  your  patient's 
vision  be  improved  to  f^,  with  a  convex  spherical  glass  of 
2  D,  over  which  you  have  placed  a  concave  cylindric  glass 
of  2  D,  with  the  axis  at  90°,  you  will  neutralize  the  re- 
fractive power  of  the  spherical  glass  in  the  meridian  of 
1 80°,  while  it  will  remain  of  the  same  refractive  power  in 
the  meridian  parallel  to  the  axis  of  the  cylindric  glass. 
Hence  it  would  be  the  same  as  a  simple  convex  cylindric 


l6o  LECTURES   OX  THE   ERRORS   Of-    REFRACTION. 

glass  of  2  D,  with  the  axis  placed  horizontal.     To  pr 
this  try  the  convex  cylindric  glass  alone,  and  see  if  you 
have  the  same  vision. 

Now,  if  we  find  that  we  require  a  stronger  concave 
cylindric  glass  than  the  one  just  illustrated,  then  select 
the  weakest  which  will  give  the  best  vision,  and  the  trial 
by  glasses  gives  us  a  case  of  mixed  astigmatism.  For 
instance,  if  we  used  a  convex  spherical  glass  of  2  D,  and 
placed  over  that  a  concave  cylindric  glass  of  3  D,  with  its 
axis  vertical,  or  at  90°,  the  refraction  of  this  combination 
would  be  obviously  for  the  vertical  meridian — the  meridian 
parallel  to  the  axis — still  convex  2  D.  In  a  horizontal 
meridian  it  would  be  (—3  D)  -  -  (-f-  2  D)  =  -  -  I  D. 
Consequently  we  would  have  a  case  of  hyperopiu  of  2  I) 
in  the  vertical  meridian,  and  a  myopia  of  i  D  in  the; 
horizontal. 

Let  us  now  test  a  case  in  which  there  is  no  improve- 
ment of  the  distant  vision,  or  it  is  diminished  with  con- 
vex classes.  We  may  then  proceed  to  try  the  cone 
glasses,  and  we  select  the  weakest  concave  spherical  that 
will  give  the  best  vision.  Then,  if  the  vision  be  improved 
by  adding  a  convex  cylindric  glass  to  the  concave  spheri- 
cal already  selected,  of  the  same  refractive  power,  but 
positive, — turning  the  axis  from  right  to  left  until  \v< 
reach  the  meridian  of  best  vision, — we  will  have  a  case 
of  simple  myopic  astigmatism.  We  may  prove  this  by 
using  the  negative  cylindric  glass  of  the  same  refractive 
power,  placing  the  axis  at  right  angles  to  the  position 
occupied  by  the  convex  cylindric  glass  used.  For,  if  we 
have  selected  a  concave  spherical  glass  of  2  D,  and  over 
this  have  placed  a  convex  cylindric  class  of  2  D,  with  the 
axis  vertical,  its  refractive  power  will  be  the  same  as  that 
of  a  concave  cylindric  glass  of  2  D,  with  its  axis  placed 
horizontal. 

Proceeding  still  further  in  our  examination,  if  we  find 


A  S  TIG  MA  T1SM.  1 6 1 

no.  improvement  with  the  convex  cylindric  glass,  we  will 
now  proceed  to  try  the  addition  of  concave  cylindric 
glasses  to  the  concave  spherical  glass  first  selected,  and 
turn  the  axis  slowly  to  the  left  until  we  find  the  proper 
meridian.  Then  find  the  weakest  concave  cylindric  glass 
that  will  give  the  best  vision,  and  we  have  a  case  of  com- 
pound myopic  astigmatism. 

I  have  found  this  method  of  testing  the  astigmatic 
•eye  the  most  reliable  ;  and  at  the  same  time  the  most 
simple  and  rapid  by  which  we  can  obtain  the  best  results, 
particularly  for  clinical  work.  It  is  usually  necessary  in 
astigmatism  that  the  accommodation  of  your  patient  be 
perfectly  at  rest.  This  condition  you  will  only  obtain 
in  complete  paralysis  of  the  ciliary  muscle  by  the  use  of 
some  mydriatic,  as  atropine.  This  is  the  best  and  most 
reliable  drug  for  this  purpose,  as  your  trial  by  glasses 
must  then  give  you  the  true  error  of  refraction.  You 
should  not  use  atropine  in  persons  over  fifty  or  sixty 
years  of  age,  nor  is  it  usually  necessary  at  forty,  as  then 
the  amplitude  of  accommodation  being  about  nil,  will  not 
interfere  with  your  tests,  and  the  results  will  give  the  total 
•error  of  refraction. 

In  reference  to  the  calculations  necessary  as  regards 
the  refraction  of  the  glasses  when  combinations  are  used, 
you  will  only  calculate  the  refraction  in  the  two  principal 
meridians,  one  being  always  parallel  to  the  axis  of  the 
cylindric  glass,  and  the  other  at  right  angles  to  that  me- 
ridian. Then  remember  in  your  result  to  always  place  the 
axis  of  the  cylindric  glass  at  right  angles  to  the  axis  of 
the  glass  used  in  the  combination. 

This  examination  of  the  visual  acuteness  and  the  cor- 
rection of  astigmatism  is  undoubtedly  the  best  and  most 
reliable,  particularly  if  the  examined  eye  be  under  the  in- 
fluence of  atropine.  But  we  should  also  confirm  the 
examination  of  the  vision  by  the  results  obtained  in  ex- 


1 62  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

amining  each  meridian  with  the  stenopaeic  slit ;  the  radiat- 
ing lines  placed  at  twenty  feet ;  by  the  method  of  retino- 
scopy  ;  and,  lastly,  by  testing  and  estimating  each  meridian 
with  the  ophthalmoscope. 

You  will  then  proceed  to  test  your  patient  with  the 
figure  representing  radiating  lines  running  in  different  di- 
rections from  a  common  point  on  a  white  ground.  They 
should  be  equidistant  and  exactly  alike. 


FIG.  77. — GREEN'S  TEST-CARD  FOR  ASTIGMATISM. 

Various  designs  have  been  devised  for  this  purpose,  as 
those  of  Javel,  Green,  and  others.  I  prefer  Green's  card 
for  this  purpose,  which  represents  the  lines  as  the  spokes 
of  a  wheel  placed  equidistant,  and  numbered  as  the  hours 
on  the  dial  of  a  clock,  in  which  the  lines  running  from 
XII  to  VI  will  be  vertical,  and  those  from  IX  to  III  will 
be  horizontal,  etc.  Or  you  may  use  the  lines  which  radiate 
like  a  fan  (Javel's),  beginning  at  the  left  end  of  the  hori- 
zontal meridian  and  spreading  out  to  the  right.  Then 


ASTIGMATISM. 


the  vertical  lines  will  be  at  90°  and  the  horizontal  lines, 
will  correspond  to  180°. 

You  will  then  ask  your  patient  which  line  he  sees  the 
best  or  most  distinctly  with  the  examined  eye,  and  which 
line  is  most  indistinct ;  but  first  correct  any  existing  error 
of  refraction  with  the  spherical  glass  that  will  give  the 
.best  vision.  In  this  way  you  correct  the  hypermetropia 
or  myopia.  Then  add  the  correcting  cylindric  glass  at 
the  proper  angle  ;  this  will  make  all  the  lines  on  the  as- 
tigmatic card  appear  alike,  placing  the  axis  of  the  cylin- 


FIG.  78. — JAVEL'S  TEST-CARD  FOR  ASTIGMATISM. 

dric  glass  at  right  angles  to  the  direction  of  the  lines  which 
are  seen  darkest  and  most  distinctly.  These  lines  are 
always  seen  in  the  meridian  of  greatest  ametropia,  pro- 
vided the  accommodation  be  at  rest — that  is,  in  the  meridian 
of  the  cornea  with  the  curve  greater  or  less  than  normal. 
You  can  remember  this  fact  and  the  reasons  for  it,  be- 
cause if  we  find  the  curvature  of  the  cornea  greater  in  the 
vertical  meridian,  then  all  the  rays  that  pass  inward  in  that 
meridian  will  cross  before  they  reach  the  retina  ;  conse- 
quently, when  they  do  strike  the  retina,  each  ray  will  over- 
lap the  other,  while  the  rays  which  pass  inward  in  the  hori- 
zontal meridian,  being  emmetropic,  will  exactly  focus  upon 
the  retina  ;  and  as  these  rays  form  the  edges  of  the  line 


164  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

they  are  seen  clearly  and  distinctly.  I  shall  illustrate  this 
to  you  more  fully  in  the  estimation  of  astigmatism  with 
the  ophthalmoscope. 

The  next  method  by  which  you  may  confirm  the  results 
of  the  two  previous  examinations  is  the  test  made  with  the 
stenopaic  slit.  This  consists  of  a  disc  of  metal,  of  the  same 
diameter  as  the  usual  test  glasses,  with  an  opening  or  slit 
in  the  centre  about  1 2  mm.  long,  having  a  slide  attached 
so  that  the  opening  can  be  made  of  any  desired  width,  the 
usual  distance  being  about  one  mm.  This  will  cut  off  all 
the  peripheral  rays  in  one  meridian,  but  allows  them  to 
pass  freely  in  the  other. 

Place  the  stenopeeic  slit  before  the  examined  eye,  with 
the  opening  horizontal,  and,  turning  it  from  right  to  left, 
find  the  position  at  which  the  patient  has  the  best  vision. 
If  in  this  meridian  you  find  V  =  |$,  then  that  meridian 
must  be  emmetropic,  and  the  lines  will  be  all  alike.  But 
if  not,  you  will  then  add  either  a  convex  or  a  concave 
spherical  glass  until  all  the  lines  are  equal  and  the  best 
vision  is  obtained.  Then  test  the  meridian  at  right  angles 
to  this  in  the  same  way,  adding  either  convex  or  concave 
glasses  as  may  be  necessary. 

If  you  require  a  glass  over  the  slit  in  each  meridian, 
one  stronger  than  the  other,  the  weakest  glass  will  give 
you  the  refraction  of  the  least  meridian,  and  the  second 
glass  that  of  the  greater,  while  the  difference  between 
them  will  give  you  the  amount  of  the  astigmatism. 

If  the  examined  eye,  with  the  stenopaeic  slit  at  180°, 
has  V  =  |f,  with  -f  fa,  and  at  90°  V  =  f#,  with  +  ,'„, 
then  you  have  hypermetropia  of  -^  in  the  horizontal 
and  yL  in  the  vertical,  meridian.  The  proper  glass 
for  correction  would  be  -f-  -jV  s-  O  +  -sV  CY^  ax's  ^o0, 
as  this  glass  will  have  the  correct  refraction  in  both  prin- 
cipal meridians. 

As  this  stenopaeic  slit  will  cut  off  all  the  peripheral 


A  S  TIG  MA  TISM.  165 

rays  in  the  meridian  at  right  angles  to  its  opening,  then  it 
measures  the  refraction  in  one  meridian  only,  cutting  off 
all  the  overlapping  rays  that  would  blur  the  edges  of  the 
letters.  If  the  meridian  be  not  emmetropic,  you  must  then 
add  a  suitable  glass  that  will  make  it  so. 

Let  us  now  proceed  to  one  of  the  final  tests  of  astig- 
matism—the use  of  the  ophthalmoscope,  which  I  have 
fully  explained  in  an  article  published  in  the  New  York 
Medical  Record,  vol.  xxxix.,  No.  24,  of  June  12,  1886, 
p.  673,  to  the  following  portions  of  which  I  will  call  your 
attention  : 

"  The  diagnosis  and  determination  of  astigmatism  with 
the  ophthalmoscope  by  the  direct  method  is  not  only  ex- 
ceedingly interesting  but  somewhat  difficult,  unless  we 
estimate  each  of  the  two  principal  meridians  separately. 
It,  then,  should  become  almost  as  easy  as  the  diagnosis  of 
simple  hypermetropia  or  myopia,  when  we  have  simply  an 
elongation  or  shortening  of  the  optic  axis. 

"  In  determining  the  simple  errors  of  refraction,  we 
take  as  our  standard  of  comparison  the  minute  vessels 
of  the  disc  or  retina,  or,  better  still,  the  delicate  tapetum 
formed  by  the  choroidal  epithelium,  and  then,  in  hyperme- 
tropia, use  the  strongest  convex  glass  behind  the  aperture 
of  the  ophthalmoscope  with  which  this  tapetum  can  still 
be  distinctly  seen.  This  will  give  the  amount  of  hyper- 
metropia ;  while  in  myopia  we  would  select  the  weakest 
concave  glass  that  will  render  the  blurred  tapetum  dis- 
tinct, and  this  glass  will  give  us  the  amount  of  myopia. 

"  Now  in  astigmatism  we  cannot  use  this  delicate 
test,  so  we  select  the  edges  of  the  optic-nerve  entrance, 
which,  passing  in  a  circle,  will  give  us  short  lines  running 
in  any  direction  ;  or  the  minute  delicate  vessels  that  you 
will  find  in  different  parts  of  the  retina  or  on  and  around 
the  optic  disc.  The  most  delicate  test  is  that  of  the  brill- 
iant white  line  running  along  the  centre  of  each  artery  of 


1 66      LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

the  retina.  If  we  take  any  of  these  points  for  observa- 
tion, and  can  decide  which  will  focus  upon  the  retina  of 
the  observer's  eye,  these  vessels  or  lines  will  give  us  the 
direction  of  the  meridian  of  greatest  ametropia,  provided 
in  all  cases  that  the  accommodation  of  the  observer  be  in 
a  state  of  complete  relaxation. 

"  We  will  precede  the  study  of  the  errors  of  refrac- 
tion caused  by  astigmatism,  by  the  supposition  that  very 
few  are  able  to  have  such  complete  control  Over  their 
accommodation  that  they  can  at  all  times  completely  relax 
it,  so  that  the  observer's  eye,  when  estimating  refraction, 
shall  be  in  a  state  of  complete  rest.  Now  this  defect  will 
make  but  slight  difference  in  estimating  myopia,  as  the 
observer's  eye  cannot  accommodate  for  convergent  rays, 
but  in  hypermetropia  it  must  be  taken  into  consideration, 
although  the  practical  results  should  be  the  same.  For 
instance,  very  few  examiners  who  are  accustomed  to  use 
the  ophthalmoscope  can  so  control  the  accommodation 
that  they  can  examine  the  fundus  of  a  hypermetropic 
eye  of  i  or  2  D  and  find  the  details  blurred  and  indis- 
tinct. But,  making  our  diagnosis  from  the  fact  that  \ve 
can  still  see  these  details  clearly,  by  placing  a  convex 
glass  behind  the  aperture,  (and  the  strongest  convex  rep- 
resents the  amount  of  total  hypermetropia)  so  we  must 
calculate  the  amount  of  astigmatism  present,  if  hyperme- 
tropic, and  only  the  individual  vessels  as  our  guide. 

"  I  shall  not  quote  the  writings  of  our  many  standard 
authors,  as  it  has  seemed  to  me  that  nearly  all  of  them  have 
dismissed  this  most  important  subject,  and  one  that  is  so 
necessary  to  the  ophthalmologist,  with  very  few  words. 
Even  our  most  illustrious  master  on  refraction,  Bonders, 
says  almost  nothing,  while  Dr.  E.  G.  Loring,  in  his  ex- 
cellent work,  lately  issued,  on  Ophthalmoscopy,  devotes 
hardly  five  pages  to  this  subject,  though  his  explanations 
are  unquestionably  the  best  and  clearest  which  it  has  been 
my  pleasure  to  read. 


A  S  TIG  MA  TISM.  1 6/ 

"  If  we  could  so  control  the  accommodation  that,  when 
using  the  ophthalmoscope,  our  eyes  would  be  in  a  state  of 
complete  rest,  as  when  under  the  influence  of  a  strong 
solution  of  atropine,  then  I  can  understand  and  appre- 
ciate the  teachings  upon  this  subject.  But  if  we  consider 
that,  with  a  large  majority  of  those  who  use  the  ophthal- 
moscope, the  accommodation  is  particularly  active  when 
examining  a  hypermetropic  eye,  we  must  study  and  calcu- 
late the  errors  of  astigmatism  in  a  somewhat  different 
manner. 

"  In  teaching  the  determination  of  astigmatism,  we 
must  only  consider  those  rays  of  light  that  are  reflected 
by  the  retina  of  the  observed  eye  after  proper  illumina- 
tion with  the  ophthalmoscope.  In  doing  so,  we  must 
estimate  separately  the  refraction  of  the  two  principal 
meridians,  at  right  angles  to  each  other  ;  the  direction  in 
which  the  rays  of  light  of  each  meridian  leave  the  cornea  ; 
and  the  direction  that  they  will  have  when  they  strike  the 
retina  of  the  observer's  eye,  after  they  have  passed 
through  the  dioptric  media  of  both  eyes. 

"  This  has  been  beautifully  shown  by  my  friend  and 
assistant,  Dr.  W.  H.  Fox,  at  our  clinics,  and  at  his  lectures 
at  the  Post-Graduate  Medical  School.  This  method,  first 
used,  I  believe,  by  Professor  H.  Knapp,  and  as  we  have 
used  it,  consists  of  small  discs  of  card-board  to  represent 
the  refractive  apparatus  of  the  observed  and  the  observer's 
eye,  while  small  threads  of  different  colors,  placed  in  dif- 
ferent planes,  represent  the  rays  of  light  in  the  two 
principal  meridians. 

"  By  this  method,  if  we  take  the  rays  of  light  from 
any  luminous  spot  in  the  retina,  passing  through  the 
dioptric  media  of  the  observed  eye,  and  then  through  that 
of  the  observer,  their  directions  and  focal  points  will  be 
the  same  as  parallel  rays  of  light  passing  through  a 
spherical  and  cylindric  lens  combined,  so  that  we  shall  find 
beyond  the  refractive  media  of  the  observer's  eye,  pro- 


lf>S  LECTURES  ON  THE   ERRORS   OF  REFRACTION. 

vided  .  it  is  emmetropic,  the  two  principal  focal  points, 
with  the  focal  interval  of  STURM  between  them  ;  'that  in 
hypermetropic  astigmatism  the  retina  of  the  observer's 
eye  lies  at  the  anterior  focal  point,  and  that  in  myopic 
astigmatism  the  retina  of  the  observer's  eye  lies  at  the 
posterior  focal  point  and,  further,  that  in  compound  astig- 
matism the  retina  is  in  front  of  the  anterior  focal  point  in 
hypermetropia  and  is  beyond  the  posterior  focal  point  in 
myopia,  while  in  mixed  astigmatism  the  retina  lies  be- 
tween the  anterior  and  the  posterior  focal  point. 

"  Now,  in  all  these  cases,  but  particularly  in  that  of 
simple  astigmatism,  which  I  shall  take  as  a  standard,  we 
will  find  that  the  image,  as  formed  upon  the  retina  of  the 
observer's  eye,  is  elongated  in  the  meridian  of  greatest 
ametropia,  consequently  all  vessels  or  lines  that  pass  in 
the  direction  of  this  meridian  will  be  clearly  seen,  pro- 
vided the  accommodation  be  at  rest,  because  the  rays 
which  define  the  edges  of  these  vessels  will  pass  outward 
through  the  emmetropic  meridian,  and  will  leave  the  eye 
as  parallel,  while  all  the  rays  that  pass  outward  in  the 
meridian  of  ametropia,  when  they  strike  the  retina  of  the 
observer's  eye,  will  simply  overlap,  so  forming  a  clear 
elongated  image.  But  in  hypermetropic  astigmatism  the 
student  will  almost  invariably  use  his  accommodation,  and 
now  he  will  see  the  vessels  in  the  emmetropic  meridian. 
The  rays  will  focus  upon  his  retina  at  the  posterior  focal 
point  exactly  at  right  angles  to  the  vessels  parallel  to  the 
meridian  of  ametropia,  and  the  rays  in  the  hypermetropic 
meridian  will  now  define  the  edges  of  the  vessels. 

"By, looking  at  the  drawings  you  will  see  in  fig.  i. 
the  stand  represented,  with  one  set  of  card-boards  and 
threads  in  position,  showing  the  direction  of  rays  of  light 
in  the  vertical  meridian,  while  in  figs.  ii.  and  iii.  the  card- 
boards and  threads  only  are  represented,  but  are  so  made 
that  they  can  be  easily  attached  to  the  stand  by  a  slot,. 


I.  VERTICAL  MERIDIAN — EMMETROPIA. 

C  *B 


II.  HORIZONTAL  MERIDIAN — HYPERMKTROPIA. 


III.  HORIZONTAL  MERIDIAN— MYOPIA. 
FIG.  79. — DIAGRAMS  OF  VERTICAL  AND  HORIZONTAL  PLANES  IN  ASTIGMATISM. 


A  S  T1GMA  TISM.  1 69 

and  then  tightened  up  by  the  nuts  on  the  screws  at  the 
ends.  These  figures  are  reduced  about  one-sixth  the 
actual  size,  and  this  method  can  be  used  to  illustrate  all 
varieties  of  refractions  and  astigmatism. 

"  Explanation  :  In  fig.  i.  X,  Y  represent  the  stand, 
with  two  uprights,  H  and  /,  on  each  end,  through  which 
the  screws  pass,  with  a  small  movable  nut  on  each  screw, 
and  by  which  the  threads  are  tightened  after  the  card- 
boards are  in  position.  Then  the  card-board  at  A  will 
represent  the  retina  of  the  observed  eye,  and  a  the  lumi- 
nous point,  B  the  refractive  apparatus,  while  Cwill  repre- 
sent the  refractive  apparatus  of  the  observer's  eye,  D  the 
position  of  his  retina,  and  E  the  position  of  the  posterior 
focal  point  in  simple  hypermetropic  astigmatism.  By 
placing  these  card-boards  in  the  stand,  with  the  rays  of  the 
two  principal  meridians  shown  by  different  colored  thread, 
they  can  be  turned  to  any  meridian  in  the  arc  of  a  circle, 
though  in  the  drawing  they  are  shown  only  in  the  vertical 
and  horizontal.  Then  if  you  combine  figs.  i.  and  ii.,  or 
figs.  i.  and  iii.,  you  will  see  that  in  no  case  can  the  rays 
from  the  luminous  point  a  form  a  point  upon  the  retina  of 
the  observer's  eye,  but  must  be  elongated  in  the  direction 
of  curvature  different  from  that  of  emmetropia. 

"  In  fig.  iii.,  representing  the  horizontal  meridian  of 
an  astigmatic  eye  whose  refraction  is  myopic,  we  find  the 
rays  of  light  in  this  meridian  or  plane  to  pass  outward 
convergent,  consequently  they  will  cross  before  they  strike 
the  retina  of  the  observer's  eye  at  D,  and  there  form  an 
elongated  image.  The  rays  passing  outward  in  the  other 
principal  meridian  will  be  parallel,  as  shown  in  fig.  i. 
They  will  exactly  focus  upon  the  retina  at  D,  and  as  these 
rays  in  this  meridian  form  the  boundary  lines  of  the  ves- 
sels in  the  opposite  meridian,  then,  in  this  case,  the  ves- 
sels which  pass  horizontally  will  be  clearly  seen.  This 
being  the  meridian  of  greatest  ametropia,  the  axis  of  the 


I/O  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

correcting  cylindric  glass  must  be  placed  at  right  angles 
to  it,  or,  in  other  words,  at  right  angles  to  the  vessels 
which  are  distinct. 

14  If  we  now  study  the  direction  of  the  rays  passing  from 
a  hypermetropic  eye,  under  the  same  conditions,  we  shall 
find  that  they  also  form  an  elongated  image  upon  the 
observer's  retina  in  the  same  meridian  of  ametropia  ;  but 
now  the  image  is  formed  by  the  rays  in  the  horizontal 
meridian  reaching  the  retina  at  D  before  they  have  come 
to  a  focus,  as  shown  in  fig.  ii.,  while  the  rays  passing  in 
the  vertical  plane,  fig.  i.,  are  parallel  and  exactly  focus 
upon  the  retina  of  the  observer's  eye. 

"  Now,  if  the  observer  is  able  to  keep  his  accommodation 
completely  relaxed,  this  proposition  is  correct,  and  he  can 
only  see  the  vessels  that  pass  in  the  horizontal  direction. 
But  as  so  few  of  us,  particularly  those  who  are  learning  to 
estimate  refraction,  can  keep  the  accommodation  at  rest 
when  divergent  rays  pass  in  the  eye,  hence,  using  the 
accommodation,  we  will  focus  all  the  rays  upon  the  retina, 
and  all  the  vessels  become  clear.  If  we  then  place  a 
convex  glass  behind  the  aperture  of  the  ophthalmoscope, 
which  takes  the  place  of  and  relieves  the  accommodation, 
we  now  change  the  rays  of  light  as  if  they  came  from  an 
eye  with  simple  myopic  astigmatism.  The  convex  glass  will 
focus  the  divergent  rays  in  the  horizontal  meridian  upon 
the  retina  ;  at  the  same  time  they  will  bend  the  parallel 
rays  in  the  vertical  meridian,  which  will  then  focus  be- 
fore they  reach  the  retina  of  the  observer's  eye.  The 
position  of  the  retina  is  now  changed  to  the  posterior 
focal  point,  and  the  vertical  vessels  can  be  seen  most 
distinct  exactly  at  right  angles  to  the  vessels  seen  with  the 
accommodation  relaxed.  The  emmetropic  meridian  is  made 
myopic  by  the  action  of  the  convex  glass,  consequently 
the  axis  of  the  correcting  cylindric  glass  must  be  placed 
parallel  to  the  vessels  most  distinctly  seen  in  hyperme- 


A  S  TIGMA  TISM.  1 7 1 

tropic  astigmatism  when  the  accommodation  or  a  convex 
glass  is  used.  The  strongest  convex  glass  by  which  these 
vessels  are  made  clear  will  represent  the  amount  of 
ametropia. 

"  These  same  rules  will  apply  in  compound  astigmatism, 
but  we  must  first  correct  the  general  refraction  in  myopia 
by  the  weakest  concave  glass  that  will  make  the  vessel  in 
any  one  meridian  distinct,  and  in  hypermetropia  by  the 
strongest  convex  glass  that  will  first  blur  the  vessels  in 
any  meridian. 

"  We  can  illustrate  these  rules  by  the  following  cases  : 
In  simple  myopic  astigmatism  the  vertical  vessels  are  dis- 
tinctly seen  through  the  aperture  of  the  ophthalmoscope, 
then  with  -  -  2  D  all  the  vessels  are  clearly  seen,  as  the 
accommodation  will  correct  the  divergence  of  the  parallel 
rays  caused  by  the  concave  glass,  hence  the  correcting 
cylindric  glass  would  be  --  2  D  ;  cyl.  axis  180°,  or  hori- 
zontal. 

"In  simple  hypermetropic  astigmatism  all  the  vessels 
can  be  seen  in  every  meridian,  but  if  we  place  a  convex 
glass,  as  -f-  2  D,  the  vertical  vessels  can  still  be  distinctly 
seen,  while  all  the  horizontal  vessels  are  blurred.  We 
now  find  that  the  correcting  cylindric  glass  will  be  --)-  2  D  ; 
cyl.  axis  90°,  or  vertical,  the  axis  now  being  parallel  to 
the  vessels  most  distinctly  seen. 

"  Let  us  now  take  a  case  of  compound  myopic  astigma- 
tism. All  the  vessels  will  appear  blurred,  and  the  weak- 
est concave  glass  which  will  make  the  vessels  in  any 
meridian  clear,  say  -  -  2  D,  will  show  the  vertical  vessels. 
Then  we  have  general  myopia  of  -  -  2  D,  and  the  axis  of 
the  astigmatic  glass  must  be  at  right  angles  to  these 
vessels.  We  then  measure  the  amount  of  the  astigmatism 
by  the  weakest  glass  that  will  make  all  the  vessels  clear, 
as  --  4  D,  and  the  difference  between  these  two  glasses 
will  give  the  amount  of  astigmatism.  Thus  the  proper 


172  LECTURES  ON    THE   ERRORS  OF  REFRACTION. 

glass  to  correct  this  case  would  be --2  D  O  ~  ~  2  D  cyl. 
axis  1 80°,  or  horizontal. 

"  But  in  a  case  of  compound  hypermetropic  astigmatism 
all  the  vessels  can  be  clearly  seen,  if  not  of  too  high  a  degree 
of  hyperopia,  as  the  accommodation  will  be  active,  and 
the  strongest  convex  glass  that  will  first  blur  the  vessels 
in  any  meridian, — as  with  +  2  D  the  vessels  in  the  hori- 
zontal meridian  begin  to  blur, — this  glass  will  represent 
the  amount  of  general  hypermetropia.  Now,  the  axis  of 
the  astigmatic  glass  must  ^parallel  with  the  vessels  which 
are  still  distinctly  seen  ;  and  as  the  strongest  convex  glass 
with  which  these  vessels  in  the  vertical  meridian  can  bese<  n, 
as  +  4  D  less  the  amount  of  general  hypermetropia,  will 
represent  the  astigmatism,  therefore  the  correcting  glass 
would  be  +  2  D  ^  +  2  D  cyl.  axis  90°,  or  vertical. 

"In  mixed  astigmatism  with  the  vertical  meridian 
myopic  and  the  horizontal  meridian  hypermetropic,  you 
will  see  the  disc  elongated  in  the  direction  of  the  myopia, 
or  vertically.  All  the  vessels  running  vertically  are 
distinct, — unless  the  accommodation  is  relaxed,  when  the 
vessels  and  all  the  details  of  the  fundus  will  be  indistinct. 
But  this  condition  is  difficult  to  accomplish,  and  so,  using 
the  accommodation,  we  can  see  the  vertical  vessels  clearly  ; 
then  the  strongest  convex  glass  through  which  they  can 
be  seen,  as  -f~  2  D,  will  represent  the  amount  of  hyper- 
metropic astigmatism.  Now  place  the  axis  of  the  correcting 
glass  parallel  to  these  vessels,  and  we  have  +  2  D,  cyl.  axis 
vertical  ;  the  hypermetropic  astigmatism  being  in  the 
horizontal  meridian.  Let  us  now  place  the  weakest  con- 
cave glass  behind  the  aperture  that  will  render  all  the 
details  of  the  fundus  clear,  as  -  -  2  D,  and  we  have  the 
amount  of  myopia.  Placing  the  axis  of  the  cylindric  glass  at 
right  angles  to  the  vessels  first  clearly  seen,  then  the  cor- 
recting concave  cylindric  glass  will  be —  2  D,  cyl.  axis  180°, 
or  horizontal,  with  the  myopic  astigmatism  in  the  vertical 


A  S  TIG  MA  TISM.  1 7  3 

meridian.      So  this   case   of   mixed    astigmatism    will    be 
corrected  by  +  2  D  cyl.  axis  90  °  ^  —  2  D  cyl.  axis  1 80  °., 

"  I  wish  the  student  to  remember  that  these  calcula- 
tions are  only  made  in  this  way  because  most  physicians 
who  use  the  ophthalmoscope  are  unable  to  control  the  ac- 
tion of  the  accommodation  ;  while  even  if  we  do  have  per- 
fect control  at  all  times,  then  we  can  only  see  the  vessels 
distinctly  that  are  parallel  to  the  meridian  of  greatest 
ametropia,  and  consequently  the  axis  of  the  correcting 
cylindric  glass  must  be  at  right  angles  to  that  meridian. 

"  I  have  been  led  to  these  conclusions  from  actual 
experience  in  the  examination  of  a  large  number  of  cases 
of  astigmatism  without  the  use  of  atropine,  and  have 
confirmed  the  diagnosis  afterward  with  atropine  and  the 
trial  by  glasses.  Again,  so  little  is  written  on  this  inter- 
esting subject,  while  I  could  give  so  many  examples  from 
my  records,  when  on  service  at  the  Manhattan  Eye  and 
Ear  Hospital,  that  have  been  studied  and  the  diagnosis 
made  by  this  method.  At  the  same  time,  I  know  from  per- 
sonal experience  that  it  is  very  difficult  to  so  master  my 
own  accommodation  as  to  obtain  the  results  given  in  our 
text-books.  Nor  can  I  speak  too  highly  of  the  ability  to 
make  a  correct  diagnosis  of  all  the  errors  of  astigmatism, 
as  in  many  cases  it  will  enable  us  to  decide  if  it  is 
necessary  to  continue  the  examination  under  the  use  of 
atropia  ;  and  it  shows  us  as  well  the  cause  of  the  apparent 
amblyopia. 

"  I  would  therefore  conclude  : 

"  That  the  direction  of  the  axis  of  the  correcting 
cylindric  glass  in  myopic  astigmatism  is  at  right  angles  to 
the  vessels  which  are  most  distinctly  seen  without  a  concave 
glass. 

"That  the  direction  of  the  axis  of  the  correcting  cyl- 
indric glass  in  hypermetropic  astigmatism  is  parallel  to  the 
vessels  which  are  most  distinctly  seen  with  a  convex  glass. 


1/4  //(  77  A'/.-V   O.Y  THE   ERRORS   OF  REFRACTION. 

"  That  these  same  rules  are  applicable  in  compound 
astigmatism,  only  we  must  correct  the  general  error  of 
refraction  first,  and  then  the  astigmatism. 

•  "  Lastly,  that  these  rules  are  presented  from  the  fact, 
as  I  believe,  that  the  largest  number  of  those  who  use  the 
ophthalmoscope  cannot  control  their  accommodation  at  all 
times,  when  divergent  rays  of  light  enter  the  observer's 
eye." 

In  conclusion,  let  me  urge  you  to  examine  all  your 
cases  carefully  with  the  three  tests  I  have  given  you  : 
that  of  the  test  letters  first  ;  then  retinoscopy  ;  and,  lastly, 
the  ophthalmoscope.  If  you  find  they  all  agree,  you 
may  be  satisfied  in  the  result  of  your  examination,  and 
proceed  to  order  the  glasses  accordingly.  But  if  these 
three  excellent  tests  do  not  agree,  then  you  are  justified  in 
urging  the  use  of  atropine.  You  may  then  make  your 
final  tests,  in  the  same  way,  that  will  in  all  probability  be 
correct,  and  you  will  relieve  your  patients  of  their  asthen- 
opia  and  discomfort  caused  by  their  error  of  refraction  due 
to  astigmatism. 


NINTH    LECTURE. 

RETINOSCOPY. 

Retinoscopy  or  pupilloscopy — The  theory  of  the  concave  mirror — The  theory  of  the 
plane  mirror — Direction  of  the  rays  in  hypermetropia — In  myopia — Diagnosis  of 
refraction  with  the  plane  mirror — In  hyperopia — In  myopia — In  astigmatism — At 
different  meridians — Advantages — Caution  in  regard  to— Its  practical  use. 

GENTLEMEN  : — The  next  method  for  the  examination 
of  the  refraction  and  confirming  the  results  of  our  previ- 
ous tests,  is  that  of  pupilloscopy,  or  the  shadow  test  as  it  is 
called.  Dr.  PARENT,  of  Paris,  uses  the  name  of  retino- 
scopy  ;  a  term  that,  I  think,  is  probably  correct,  as  I  shall 
try  to  show  you  that  the  phenomenon  which  is  seen  by  this 
test  arises  from  the  illumination  of  the  retina  and  not  from 
any  participation  of  the  pupillary  space  or  the  shadow  of 
the  iris.  That  the  iris  does  throw  a  shadow  upon  the 
illuminated  portion  of  the  retina  I  have  no  doubt,  but 
only  when  the  illuminated  portion  passes  over  the  retina, 
beyond  the  line  of  sight ;  consequently  the  shadow  of  the 
iris  cannot  be  seen  by  the  examiner. 

The  first  mention  of  this  test  in  refraction  is  in  DON- 
DERS,  (p.  490,  edition  1864),  whose  attention  was  called 
to  it  by  his  friend  Bowman,  but  no  special  use  was 
made  of  the  method  at  that  time.  Afterward  Dr.  Cuiguet, 
of  Lille,  demonstrated  its  value  in  the  diagnosis  of  all  the 
errors  of  refraction  and  astigmatism.  In  his  investigations 
he  used  a  concave  mirror,  and,  although  the  final  results 
may  be  the  same,  I  would  advise  you  to  learn  this  method 
of  diagnosis  by  means  of  the  plane  mirror,  as  you  will 
find  it  much  more  easily  understood. 

175 


LECTURES  ON  Till:    EKKORS  OF  KEh'KACTJOX. 


In  the  use  of  the  concave  mirror,  such  as  you  have  on 
your  ophthalmoscope,  or  of  one  of  greater  diameter  made 

for  this  purpose,  you  must 
remember  that,  being  con- 
cave, the  position  of  your 
illumination   lies  in  front 
of  the  mirror  at  its  focal 
point.     From    this   point 
the    rays    enter   the    ex- 
amined   eye    in    a   diver- 
o  gent     direction.       Then, 
;  as   you    examine  an    eye 
_   by  this  method,  the  light 
>  proceeding    from    an    in- 
u  verted  image  of  the  flame 
a  in   front   of  your   mirror, 
a  as   the    mirror   is    turned 
5  on  its  vertical  axis  to  the 
:  right  or  left,  the  position 
p  of  the  flame  will  move  in 
•  the    same    direction.     As 
°[  these  rays  of  light  reach 
<§  the  retina,  moving  on  the 
2  nodal   point   as  a  centre, 
the  illuminated  portion  of 
the    retina  will    move    in 
the  opposite  direction. 

Let  me  illustrate  this 
to  you  by  the  diagram  in 
the  horizontal  plane  : 

The  rays  of  light  from 
the  lamp  at  A  will  fall 
upon  the  concave  mirror  B,  coming  to  a  focus  at  the  point 
C;  they  will  then  diverge  and,  passing  through  the  dioptric 
media,  will  illuminate  the  retina  at  E.  Now,  if  we  turn  the 


RETINOSCOPy. 


177 


\ 


mirror  on  its  vertical  axis  to  the  left  at  JB1,  the  point  of 
illumination  will  also  move  to  the  left  at  C\  and  the  axial 
rays,  turning  upon  the  nodal  point 
at  D,  will  cause  the  illuminated  por- 
tion of  the  retina  to  move  to  the 
right,  at  El ;  consequently,  with  a 
concave  mirror,  the  illuminated  por- 
tion of  the  retina  will  move  in  the 
direction  opposite  to  that  in  which 
the  mirror  is  turned. 

Now  in  the  use  of  this  means  of 
diagnosis,  we  must  depend  upon  the 
rays  proceeding  from  the  retina,  as 
they  are  reflected  back  toward  the 
examiner  ;  then,  if  the  refraction  of 
the  dioptric  media  be  emmetropic, 
the  reflected  rays,  as  they  proceed 
from  the  examined  eye,  will  be  par- 
allel, and  the  reflex  will  not  have 
any  decided  movement,  but  with  a 
slight  tendency  to  move  in  the  oppo- 
site direction  to  which  the  mirror  is 
turned.  In  hypermetropia,  the  reflex 
will  move  in  the  opposite  direction  ; 
but,  if  we  have  those  movements  of 
the  reflex  in  the  same  direction  in 
which  the  mirror  is  moved,  unless 
of  very  slight  degree,  we  must  have 
myopia. 

You  will  see  by  this  diagram  (fig.  \  I  hi 
81)  that,  as  the  rays  proceed  from  the 
illuminated  portion  of  the  retina  at 
L,  they  will  emerge  from  the  eye  convergent,  as  they 
come  from  a  point  beyond  the  refraction  of  the  dioptric 
system.  We  have  a  real  image  of  the  reflex,  seen  in 


178  LECTURES  ON  THE  ERRORS  OF  REFRACTION, 

front  of  the  observer,  at  the  focal  distance  of  the  myopia 
at  M. 

Then,  if  the  illuminated  portion  moves  to  D  or  Z,a  the 
real  image  will  move  to  the  right  or  left,  as  the  case  may 
be  ;  or,  as  the  mirror  is  turned,  we  now  see  the  movement 
as  an  aerial  image  at  Ml  or  M3  respectively.  As  the  re- 
flex from  Ll  will  be  seen  at  Ml  and  the  reflex  from  L* 
will  be  seen  at  M2,  so,  as  the  mirror  moves  to  the  left,  the 
reflex  also  seems  to  move  to  the  left,  and  when  the  mirror 
turns  to  the  right  so  also  does  the  image  seem  to  move. 

As  I  have  stated  to  you,  these  movements,  either  with 
or  against  the  movements  of  the  mirror,  may  show  very 
slight  myopia,  (less  than  ^)  emmetropia,  or  hyperopiu. 
But  if  you  place  a  convex  spherical  glass  before  the  exam- 
ined eye,  so  as  to  render  the  refraction  still  more  myopic, 
by  converging  the  emergent  rays,  and  the  reflex  still 
moves  in  the  same  direction,  you  may  be  positive  of  my- 
opia. But  if  you  find  that  the  reflex  moves  in  the  opposite 
direction  to  which  the  mirror  is  turned,  with  the  weak 
spherical  glass  before  the  eye,  you  will  have  hypermetro- 
pia  ;  as  now  the  rays  from  the  retina  proceed  as  if  coming 
from  a  point  inside  of  the  focal  distance  of  the  dioptric 
media,  with  the  emergent  rays  divergent.  The  reflex  will 
appear  as  a  virtual  image  coming  from  the  negative  focal 
point  of  the  dioptric  media. 

Having  told  you  that  the  use  of  the  plane  mirror  was 
the  easier  to  understand,  I  will  explain  the  method  pf 
using  it  and  the  theory  upon  which  I  think  the  move- 
ments of  the  reflex  are  based.  By  the  use  of  the  plane 
mirror  you  will  find  that  all  the  movements  of  the  illu- 
minated portion  of  the  retina  are  reversed.  The  rays 
from  your  point  of  illumination,  though  coming  from  the 
lamp  at  the  side  of  or  above  your  patient,  will  proceed  as  if 
they  came  from  a  point  behind  the  mirror  equal  to  the 
distance  of  the  lamp  from  the  mirror.  If  you  are  seated 


RETINOSCOPY. 


179 


40  inches  from  the  examined  eye  and  lamp,  then  the  re- 
flected rays  from  the  mirror  will  enter  the  examined  eye 
as  if  they  came  from  a  point 
80  inches  from  it  and  will 
be  almost  parallel. 

Then  as  these  parallel 
rays  come  from  this  dis- 
tant point,  and  as  the  mir- 
ror is  turned  to  the  right, 
the  point  of  illumination 
will  move  to  the  left,  or 
when  to  the  left  the  light 
moves  to  the  right  and  will 
not  turn  upon  the  nodal 
point  of  the  examined  eye, 
but  will  pass  inward  and 
illuminate  the  retina.  This 
illuminated  portion  will 
move  on  the  retina  in  the 
same  direction  as  the  mir- 
ror is  turned,  without  re- 
gard to  the  condition  of  the 
refraction  of  the  examined 
eye.  You  will  now  make 
your  diagnosis  of  the  refrac- 
tion by  the  emergent  rays, 
which,  you  will  see,  are  in- 
fluenced by  the  refraction 
of  the  dioptric  media,  as  it 
may  be  emmetropic,  my- 
opic, or  hypermetropic. 

Let  us  examine  this  dia- 
gram, which  will  show  you 
the  direction  of  the  rays  in  the  horizontal  plane  ;  at  the  same 
time  you  must  remember  that,  if  there  be  no  astigmatism, 


180  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

the  rays  will  be  the  same  in  all  meridians  or  planes  of  the 
eye.  Now  you  have  the  plane  mirror  placed  at  the  point 
y,  reflecting  the  rays  of  light  from  the  lamp  at  A,  as  if 
they  came  from  a  point  behind  the  mirror  equal  to  the 
distance  of  the  lamp  from  the  mirror.  This  will  illumi- 
nate the  examined  eye  with  a  bundle  or  cylinder  of  light, 
composed  of  parallel  rays  around  the  axial  ray  X\  starting 
from  a  point  behind  the  mirror  and  passing  through  the 
dioptric  media,  they  will  illuminate  the  retina  at  E.  If  you 
now  turn  the  mirror  on  its  vertical  axis  to  the  right  )'. 
the  cylinder  of  reflected  rays  from  the .  mirror  will  also 
move  to  the  right  and  the  axial  ray  will  be  at  X3,  with  tin- 
retina  illuminated  at  E*  ;  and  when  the  mirror  is  turned 
to  the  left  Fa,  with  the  axial  ray  at  X\  we  have  the  retina 
illuminated  at  E  *.  Thus  with  the  plane  mirror  we  find  that 
the  illuminated  portion  of  the  retina  moves  in  the  same 
direction  as  the  mirror  is  turned.  In  emmetropia,  as  the 
rays  will  pass  outward  from  the  eye  in  the  same  direction 
as  they  entered,  there  will  be  very  slight,  if  any,  move- 
ments of  the  reflex,  as  they  come  from  a  point  on  the 
retina  equal  to  the  focal  distance  of  the  dioptric  media  ; 
but  the  reflex  will  appear  very  bright,  with  almost  no 
movement  or  so-called  shadow. 

Let  us  now  study  the  appearance  of  the  reflex  in  cases 
of  ametropia  of  more  than  -fa-,  in  which  the  so-called  shadow 
appears,  and  from  which  this  test  takes  its  name.  It  was 
supposed  that  the  dark  portion  which  appears  in  the  pupil- 
lary space  following  the  illuminated  portion,  as  moved  in 
different  directions,  was  due  to  the  shadow  of  the  iris  fall- 
ing upon  the  retina,  as  the  iris  would  cut  off  the  rays  of 
light.  But  I  think  we  can  prove  that  it  is  due  to  a  different 
cause,  and  that  the  name  shadow  test  is  not  the  correct  one, 
as  has  been  stated  in  the  text-books  of  ophthalmology. 

In  support  of  this  theory,  and  to  demonstrate  to  you 
what  does  cause  this  so-called  shadow,  let  us  again  look  at 


RE  TI NO  SCOP  Y.  1 8 1 

fig.  82,  and  we  shall  find,  taking  the  light  from  A  and 
striking  upon  the  mirror  Y,  a  cylinder  or  bundle  of  rays 
projected  against  the  examined  eye  O,  with  its  axial 
ray  shown  by  the  line  X\  This  being  refracted  by  the 
dioptric  media,  we  find  the  retina  illuminated  at  E. 
When  this  axial  ray  corresponds  with  the  optic  axis,  we 
find  the  pupillary  space  simply  illuminated  ;  the  return  rays, 
in  this  case,  being  slightly  divergent,  and  following  almost 
the  same  path  as  they  entered  the  eye  O.  If  we  now  turn 
the  mirror  to  the  right,  with  the  cylinder  of  light  turning  in 
that  direction,  we  illuminate  the  retina  at  E1.  The  right 
side  of  the  cylinder,  being  cut  off  by  the  iris,  forms  a 
shadow  of  the  latter  on  the  retina  at  D ;  consequently  can- 
not be  seen  by  the  examiner's  eye  placed  behind  the  mir- 
ror. The  same  fact  is  shown  in  the  diagram  with  the 
cylinder  of  light  turned  to  the  left,  and  the  retina  illumi- 
nated at  E2,  with  the  shadow  of  the  iris  at  D*  behind  the 
pupillary  space. 

We  can  now  leave  out  the  shadow  of  the  iris  and  in- 
quire :  What  does  cause  this  "  shadowy  edge  of  the  circles 
of  diffusion  that  appear  to  pass  across  the  pupillary 
space " ? 

As  our  cylinder  of  rays  passes  to  the  right  (fig.  82), 
following  the  axis  X2,  and  as  the  edges  of  this  cylinder  of 
light  uncover  the  pupillary  space  to  the  left,  the  dark 
portion  of  the  retina  at  B,  not  illuminated,  will  appear  to 
the  left  of  the  pupil,  following  the  illuminated  portion  of 
the  retina  as  it  passes  to  the  right.  It  appears  as  a  dark 
shadow  coming  from  behind  the  iris,  and  passing  in  the 
same  direction  as  the  mirror  is  turned.  In  the  examined 
eye,  if  hypermetropic,  as  these  rays  of  light  are  refracted 
by  the  dioptric  apparatus,  and  are  again  reflected  by 
the  retina,  the  return  rays,  being  only  slightly  divergent, 
pass  outward  in  almost  the  same  path  in  which  they  en- 
tered. They  will  not  interfere  with  the  view  of  the  dark 


182 


LECTURES  ON  THE  ERRORS  OF  REFRACTION. 


parts  of  the  retina,  so  that  we  can   readily  appreciate  the 

movements  of  the  illuminated  portion,  formed  of  circles 

of  diffusion  by  the  lamp  at 
A.  When  the  mirror  is 
turned  to  the  left,  the 
shadow  of  the  iris  is  at 
D\  and  the  non-illuminated 
portion  of  the  retina  at  It1 
appears  as  the  shadowy 
edge. 

From  the  above  de- 
scription of  the  appearance 
of  the  retina  in  the  hyper- 
metropic  eye,  the  position 
of  the  source  of  the  illumi- 
nation lies  behind  the  mir- 
ror ;  and  as  the  mirror  is 
turned  upon  the  vertical  or 
the  horizontal  axis,  the  axial 
ray  does  not  pass  through 
the  nodal  point  of  the  ex- 
amined eye  ;  as  is  the  case 
when  you  use  the  concave 
mirror,  where  the  source 
of  illumination  is  in  front 
of  the  mirror,  and  moves  in 
the  direction  in  which  it  is 
moved.  Therefore,  with 
the  rays  divergent  as  they 
enter  the  eye,  the  axial  ray 
must  turn  on  the  nodal 
point,  and  we  have  the 

circles  of  diffusion  on  the  retina  moving  in  an  opposite 

direction. 

In  myopia  we  find  the  retina  illuminated  by  the  same 


RE  TI NO  SCOP  Y.  183 

cylinder  of  rays  from  the  mirror,  moving  on  the  retina  as 
the  mirror  is  turned — though  they  illuminate  the  retina 
after  they  have  passed  the  focal  point, — with  the  axial  ray 
at  X  or  K  As  the  rays  from  the  mirror  illuminate  the 
retina  at  JV\  the  return  rays  now  passing  through  a  re- 
fractive system  whose  focal  point  is  beyond  that  of  the 
dioptric  apparatus,  the  emergent  rays  are  convergent,  and 
the  real  image  of  the  circles  of  diffusion  will  be  seen  at  a, 
appearing  to  light  up  the  entire  pupillary  space.  Let  us 
now  turn  the  mirror  to  the  right,  and  we  have  the  retina 
illuminated  at  TV3,  but,  the  emergent  rays  having  a  posi- 
tive focus  at  a,  the  axial  ray  will  turn  on  the  nodal  point 
at  P,  and  the  real  image,  at  a,  must  move  to  the  left,  as 
at  a\  and  we  see  the  dark  portion  of  the  retina  at  B 
forming  the  shadow.  It  appears  to  follow  the  inverted 
image  a,  to  a1,  and  is  seen  by  the  examiner  as  soon  as  the 
image  of  the  circles  of  diffusion  at  a  shall  have  passed  the 
area  of  the  pupil  on  the  right  side,  and  follows  it,  as  it 
moves  to  the  left,  in  a  direction  opposite  to  that  in  which  the 
mirror  is  turned.  This  is  an  inverted  aerial  image  of  the 
illuminated  portions  of  the  fundus.  The  axial  ray,  Y,  Y, 
shows  the  cylinder  of  light  when  moved  to  the  left,  with 
the  retina  illuminated  at  Nz,  and  as  the  aerial  image 
moves  to  the  right,  the  shadowy  edge  formed  by  the  non- 
illuminated  part  of  the  retina  at  Bl  will  follow  it. 

I  shall  endeavor  to  explain  to  you,  as  we  take  up  each 
subject,  that,  in  hypermetropia,  with  the  plane  mirror,  the 
retinal  reflex  follows  the  movement  of  the  cylinder  of 
light,  and  appears  to  be  followed  by  the  dark  portions  or 
non-illuminated  parts  of  the  retina  ;  and  that  in  myopia, 
having  a  real  image  of  the  retinal  reflex,  at  the  focal 
point  of  the  dioptric  apparatus,  formed  by  the  emergent 
rays,  the  image  must  pass  to  the  right  as  the  mirror 
is  turned  to  the  left :  in  other  words,  the  retinal  image 
moves  in  an  opposite  direction. 


1 84  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

In  using  this  test  to  decide  your  errors  of  refraction, 
some  oculists  advise  that  you  should  so  place  the  ex- 
amined eye  that  the  optic  disc  will  be  directly  behind 
the  pupillary  space.  I  do  not  think  that  this  is  necessary, 
nor  exactly  correct,  as  the  refraction  of  the  eye  may  be 
different  at  the  region  of  the  macula  than  at  the  nerve 
entrance,  as  cases  have  been  recorded.  So  I  would  ad- 
vise you  to  test  your  cases  as  near  the  macula  as  possible, 
by  having  your  patient  look  a  little  to  one  side  or  above 
your  eye.  If  you  can  dilate  the  pupil  and  stop  the 
action  of  the  accommodation  by  the  use  of  atropine,  your 
examination  will  be  much  more  correct ;  though  the  ac- 
commodation has  very  little  influence  on  the  result  if  you 
examine  your  case  in  a  dark  room.  You  will  then  have  a 
very  satisfactory  test,  even  in  cases  of  hypermetropia  with 
spasm  of  the  accommodation.  I  would  also  advise  you  to 
correct  any  error  of  your  own  refraction  by  proper  glasses. 

With  these  precautions,  what  will  be  the  result  of 
your  examination  in  cases  of  ametropia,  where  the  optic 
axis  is  either  too  long  or  too  short,  as  in  myopia  or  hyper- 
metropia ?  We  shall  find  first  that,  if  the  position  of  the 
retina  be  not  at  the  focal  point  of  the  dioptric  media, 
the  rays  of  light,  as  they  illuminate  the  examined  eye,  will 
fall  upon  the  retina  before  they  have  come  to  a  focus,  as  in 
hypermetropia,  or  after  they  have  passed  the  focal  point, 
as  in  myopia,  and  the  illuminated  portions  of  the  retina 
will  be  a  round  spot,  with  indistinct  edges,  formed  by  the 
circles  of  diffusion. 

You  can  use  this  fact  as  one  of  your  means  of  diag- 
nosis, as  the  degree  of  luminosity  of  the  reflex  will  show 
the  degree  of  ametropia.  The  greater  the  luminosity,  the 
nearer  the  refraction  of  the  examined  eye  will  be  to  that  of 
emmetropia.  This  is  well  shown  in  the  higher  degrees  of 
hypermetropia  and  myopia,  where  the  emerging  rays  are 
either  very  divergent  or  very  convergent,  and  consequently 


RE  TI NO  SCOP  Y.  185 

an  insufficiency  of  rays  to  enter  the  examiner's  eye,  to 
enable  him  to  appreciate  the  movements  of  the  reflex. 

This  degree  of  brightness  in  the  reflex,  due  to  the  re- 
fraction, is  caused  by  the  fact  that,  when  the  retina  of  an 
emmetropic  eye  is  illuminated  by  the  mirror,  the  entering 
rays  form  a  clear,  bright  image  on  the  retina  ;  while  in 
ametropia,  as  I  have  just  stated,  the  reflex  is  formed,  not 
by  a  clear  image  of  the  flame,  but  by  the  circles  of  diffusion 
on  the  retina  caused  by  the  ametropia. 

In  the  hypermetropic  eye,  as  they  reach  the  retina  in 
front  of  the  focal  point,  the  rays  from  a  plane  mirror  will 
form  a  round  spot,  moving  in  the  same  direction  as  the 
mirror,  and  moves  as  it  rotates  to  the  right,  the  shadow 
of  the  iris  on  that  side,  will  cut  off  a  portion  of  the  illumi- 
nated space,  but  cannot  be  seen  by  the  examiner.  Now, 
as  the  reflex  passes  to  the  right,  the  portion  of  the  retina 
not  illuminated  comes  behind  the  pupillary  space,  and  we 
have  the  dark  appearance, — simply  a  portion  of  the  pupil- 
lary space.  This  seems  to  come  from  behind  the  iris, 
opposite  to  the  side  toward  which  you  are  moving  the 
cylinder  of  light,  by  turning  the  mirror,  and  moves  in  the 
same  direction. 

This  is  the  shadow  which  gives  this  test  its  name. 
Thus  we  see  that,  when  the  axial  ray  X3,  (fig.  82)  is  directed 
to  a  point  on  the  retina,  at  E2,  the  left  side  of  the  bundle  of 
rays  will  be  cut  off  by  the  iris,  and  the  pupillary  space  will 
appear  dark  on  the  opposite  side.  The  same  result  ob- 
tains when  the  axial  ray  X2,  is  directed  toward  the  point 
on  the  retina  at  E\  Consequently  the  shadow  of  the 
iris  cannot  be  seen,  and  the  dark  part  of  the  retina  will 
appear  to  move  in  the  same  direction  as  the  light  is  turned. 

But  it  is  not  only  this  dark  portion  of  the  retina  that 
seems  to  move,  but  we  notice  that  the  illuminated  part  of 
the  retina  moves  also,  and  in  the  same  direction,  because, 
as  the  rays  are  reflected  from  the  retina  of  the  hyperopic 


1 86 


LECTURES  ON  THE  ERKORS  OF  REFRACTION. 


eye,  they  pass  outward  in  a  divergent  direction,  as  shown 
in  this  diagram  : 

These  emergent  rays   ap- 
pear to  come  from  a  point  be- 
hind the  retina  and  the  image 
is    erect,   as   if   we   illuminate 
that  portion  of  the  retina  at  Ll, 
—by  turning  the  mirror  to  the 
right, — the  image  will  appear 
to  be  at  m*,  in  the  same  direc- 
§  tion  the  mirror  is  turned  ;  or, 
&  in  which  if  we  turn  the  mirror 
g  to  the  left,  as  at  Z,a,  the  rays 
£  will   appear  to   proceed   from 
«  the  point  ml. 

In  myopia,  with  the  plane 
mirror,  we  have  the  opposite 
effect,  as  the  emergent  rays 
from  the  retina,  as  they  are 
refracted  outward,  are  conver- 
8  gent ;  so  that  if  the  myopia 

5  be  of  a  greater  degree  than 
£  -fa  these    rays   will    converge 
i  to  the  punctum  remotum  and 

oo 

6  there    form    an    aerial    image 
"  (inverted)   of   the    retinal    re- 
flex,    with      the      axial      ray 
turning    on    the    nodal   point. 
Consequently,     as     the     illu- 
minated     portion      of       the 
retina    moves    to    the    right, 
the  aerial    image  as   seen  by 
the    examiner    will    move    to 

the  left,  and    the    curved   shadowy   portion  of  the   non- 
illuminated    retina    will    appear    to    move    in    the    same 


RETINOSCOPY. 


I87 


direction.      I  would  illustrate  this  to  you  by  the  following 
diagram. 

You  will  notice  that  the 
rays  from  the  illuminated  por- 
tion of  the  retina,  at  L1,  when 
the  mirror  is  turned  to  the  left, 
converge  to  the  point  mr,  and 
those  from  L2,  at  the  point  m*. 
Hence,  in  myopia  the  retina 
being  illuminated  the  same  as 
in  emmetropia  or  hyperme- 
tropia,  the  emergent  rays, 
having  a  focal  point,  must 
turn  on  the  nodal  point  of  the 
refractive  apparatus  at  D,  and 
appear  to  move  in  an  opposite 
direction. 

To  form  a  diagnosis,  then, 
of  the  refractive  condition  of 
an  examined  eye,  by  the 
method  of  retinoscopy  with 
the  plane  mirror,  it  will  only 
be  necessary  to  note  that,  if 
the  retinal  reflex  moves  in  the 
same  direction  in  which  the 
mirror  is  turned,  on  its  vertical 
or  horizontal  axis,  you  have 
hypermetropia ;  and  that  the 
strongest  convex  glass  placed 
before  the  eye,  as  near  the 
nodal  point  as  possible,  which 
will  stop  the  movements  of 

the    reflex,    will    measure    the    amount    of    the    existing 
hypermetropia. 

Again,  if  the  retinal   reflex  and  the  so-called  shadow 


1 88 


LECTURES  ON  THE  ERRORS  OF  REFRACTION. 


move  in  an  opposite  direction,  we  have  myopia  ;  and 
the  weakest  concave  glass  placed  before  the  examined 
eye,  as  near  the  nodal  point  as  pos- 
sible, will  give  the  measure  of  the 
myopia. 

In  using  this  test  you  must  re- 
member that  the  examiner's  eye  is 
placed  at  about  40  inches  from  the 
examined  eye,  so  that  the  rays  com- 
ing from  a  myopic  eye  of  low  degree, 

%    i.  e.,  less  than  -A-,  cannot  form  an  in- 

. 
verted  aerial   image  in  front  of  the 

°  observer.     The  converging  rays  will 

°  focus  in  front  of  his  retina,  and  the 

g  image  on  the  observer's  eye  will  follow 

^  the  direction  of  the   axial   ray  from 

o  . 

>    the  examined  eye. 

You  will  understand  this  by  ref- 
g    erence  to  this  diagram,  showing  the 
horizontal    meridians  of    the    exami- 

e 

£  ner's  and  the  examined  eye.  When 
the  reflex  comes  from  the  point  a  in 
the  eye  X,  the  cone  of  light,  as  shown 
by  the  lines,  will  enter  the  eye  Y 
convergent,  and,  being  refracted,  will 
form  circles  of  diffusion  on  the  retina 
of  the  examiner's  eye  at  B.  As  we 
move  the  reflex  to  the  left  at  c,  the 
emerging  cone  of  light  with  its  axial 
ray  will  move  to  the  right  and  form 
a  diffused  point  of  light  on  the  ex- 
aminer's eye  at  D.  This,  by  a  well- 
known  law  of  the  projection  of  the  image,  will  appear  to 
be  at  the  left,  in  the  position  of  c.  The  reflex  moves  in 
the  same  direction  in  low  degrees  of  myopia. 


RE  TIN 0 SCOP  Y.  1 89 

How,  then,  can  you  decide  between  emmetropia,  hyper- 
metropia,  or  a  low  degree  of  myopia  ?  If  you  will  place  a 
convex  lens  of  i  D  before  the  examined  eye,  when  you 
find  that  the  reflex  moves  in  the  same  direction  as  the 
mirror  is  turned,  and  it  still  follows  the  movements  of  the 
mirror,  you  must  have  hypermetropia.  This  glass  would 
tend  to  make  an  emmetropic  eye  sufficiently  myopic  to 
change  the  movements  of  the  reflex.  Then  try  a  convex 
glass  of  .75  D,  and  if  the  image  moves  in  the  opposite 
direction  you  must  have  myopia,  as  with  +  .75  D  added 
to  even  a  myopia  of  .25  D  would  make  the  rays  cross  in 
front  of  the  examiner's  eye,  showing  myopia. 

Should  you  wish  to  make  all  your  calculation  exactly 
correct,  you  must  add  i  D  to  the  correcting  glass  in 
myopia  ;  and  in  hypermetropia  subtract  i  D,  to  find  the 
amount  of  total  error  of  refraction. 

Or,  we  may  simply  move  the  position  of  the  examiner 
back  to  a  point  beyond  which  it  is  almost  impossible  to 
have  a  myopia  that  would  cause  any  possible  symptoms 
of  asthenopia.  As  if  we  have  a  myopia  of  •£-$,  by  moving 
the  mirror  back  from  the  patient  beyond  60  inches  you 
will  then  have  the  movements  in  the  opposite  direction. 
This  is  one  of  the  advantages  of  the  use  of  the  plane 
mirror,  and  by  this  method  of  altering  the  position  of  the 
mirror  you  may  measure  the  degree  of  myopia.  The 
movements  of  the  reflex  will  stop  when  the  mirror  is 
placed  at  the  point  of  convergence  of  the  emergent  rays. 
To  measure  the  myopia,  if  you  have  the  movements  in 
the  opposite  direction,  you  may  bring  the  mirror  nearer  the 
examined  eye  until  the  movements  either  cease  or  become 
very  uncertain.  Then  the  distance  of  the  mirror  from  the 
nodal  point  of  the  eye  will  give  the  degree  of  myopia,  as, 
if  the  movements  stop  at  20  inches,  then  the  ametropia 
equals  ^,  at  10  inches  yL,  and  so  on. 

Having  then  decided  that  you  have  a  case  of  ametropia 


190  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

by  the  test  of  retinoscopy,  you  can  readily  estimate  the 
amount  of  the  error  of  refraction  by  placing  a  correcting 
glass  before  the  examined  eye,  as  near  as  possible  to  the 
nodal  point,  or,  we  will  say,  about  in  the  position  of  the 
glass  of  spectacles  when  worn.  Then  observe  the  move- 
ments of  the  reflex  as  it  passes  across  the  pupillary  space, 
and  the  glass  which  will  cause  these  movements  to  cease,— 
or  become  so  uncertain  that  we  cannot  tell  positively  in 
which  direction  the  movements  are, — will  represent  the 
condition  of  refraction  in  the  examined  eye. 

Let  us  examine  first  an  emmetropic  eye  in  which  the 
reflex  is  very  bright,  the  movements  very  rapid  and  in 
the  same  direction  in  which  the  mirror  is  turned.  Then 
if  the  examiner  be  seated  at  about  40  inches  from  the 
patient,  place  a  convex  glass  of  -£$  before  the  examined 
eye,  and  find  that  the  movements  are  in  an  opposite 
direction,  he  will  have  emmetropia.  But  if  the  reflex 
be  not  so  bright,  with  the  movements  still  in  the  same 
direction  that  the  mirror  is  turned,  we  must  have  hyper- 
metropia.  Then  place  stronger  convex  glasses  before 
the  examined  eye,  and  if  the  movements  be  still  in  the  same 
direction,  the  strongest  convex  glass  which  will  stop  the 
movements  of  the  retinal  reflex,  or  make  them  uncertain, 
will  represent  the  total  amount  of  existing  hypermetropia 
in  the  examined  eye. 

Now,  if  the  movements  of  the  retinal  reflex  are  in  an 
opposite  direction,  then  we  must  have  myopia,  and  we 
will  proceed  as  before  to  place  concave  glasses  before  the 
examined  eye  until  the  movements  of  the  retinal  reflex 
stops  or  becomes  uncertain  ;  and  the  weakest  concave 
glass  that  will  produce  this  effect  will  represent  the 
amount  of  existing  myopia  in  the  examined  eye. 

This  method  is  very  simple,  and  with  a  little  practice, 
particularly  with  the  pupil  dilated  with  atropine,  will  soon 
enable  you  to  make  a  very  nearly  porrect  estimate  of  the 


RE  Tl 'NO  SCOP  Y.  1 9 1 

errors  of  refraction,  both  of  myopia  and  hypermetropia. 
As  a  test  to  confirm  your  previous  results  with  the  test 
glasses,  Snellen's  letters,  and  the  ophthalmoscope,  it  is 
very  reliable  and  of  great  service  to  the  ophthalmologist. 

This  brings  us  to  the  diagnosis  of  astigmatism  by 
retinoscopy,  and  if  you  will  remember  this  rule,  you  can 
easily  estimate  the  astigmatic  error  :  Simply  test  the  two 
principal  meridians  of  the  examined  eye,  separately,  in  the 
manner  explained  above. 

When  we  illuminate  the  eye  with  the  plane  mirror,  and 
rotate  the  mirror  on  its  vertical  or  its  horizontal  axis,  we 
will  notice  the  movements  of  the  reflex  as  it  passes  across 
the  pupillary  space,  followed  by  the  shadowy  crescent.  If 
these  movements  are  with  the  mirror  in  the  vertical  or 
horizontal  meridians,  then  they  must  show  hypermetropia  ; 
or,  if  against  the  movements  of  the  mirror,  myopia. 
After  testing  each  meridian  in  this  manner,  noting  the 
direction  and  rapidity  of  the  movements,  you  will  place  a 
convex  or  a  concave  glass  before  the  eye,  according  to 
the  condition  of  refraction  shown.  Then,  if  there  is  any 
difference  in  the  refraction  of  these  two  meridians,  the 
spherical  glass  will  only  correct  one  meridian,  and  will 
represent  the  amount  of  error  of  refraction  in  that  merid- 
ian, leaving  the  other  still  uncorrected.  You  will  then 
proceed  to  add  a  stronger  glass  until  the  error  is  corrected 
in  the  other  meridian,  and  the  difference  between  the  two 
glasses  will  be  the  amount  of  astigmatism. 

In  making  these  calculations,  leave  all  the  other 
meridians  out  of  the  examinations.  As  you  correct  one 
meridian,  you  must,  if  there  be  astigmatism,  either  under- 
or  over-correct  the  meridian  at  right  angles  to  the  one  you 
are  testing.  Remember,  also,  to  place  the  axis  of  the 
correcting  cylindric  glass  at  right  angles  to  the  meridian 
you  have  tested  by  retinoscopy. 

If  we  have  a  difference  in  the  refraction  of  the  vertical 


192  LECTURES  ON  THE   ERRORS  OF  REFRACTION. 

meridian  from  that  of  the  horizontal,  we  will  notice  that 
the  spherical  glass  placed  before  the  eye  will  correct  the 
movements  in  one  meridian,  while  in  the  meridian  at 
right  angles  to  it  we  require  a  stronger  glass.  If  you  find 
that  the  movements  in  the  vertical  meridian  cease  with 
+  ^,  and  that  in  the  horizontal  meridian  we  require  -f  ,'„, 
then  we  have  a  hypermetropia  of  .,'„  in  the  vertical  and 
-j^  in  the  other  meridian,  or  an  astigmatism  of  ^0  in  the 
horizontal  meridian.  The  glass  that  would  make  both 
meridians  emmetropic  is  +  -^  O  ~f~  ^V  CV^  ax's  vertical. 

You  will  notice  by  this  that  the  movement  of  the 
reflex  and  also  of  the  shadowy  edge  are  along  the 
ametropic  meridian  ;  that  the  shadowy  edge  is  parallel 
with  the  axis  of  the  cylindric  glass  ;  and  that  the  spherical 
glass  placed  before  the  eye  which  will  stop  these  move- 
ments, in  the  meridian  tested,  will  show  the  refraction. 

As  you  test  each  meridian  separately,  it  will  make  no 
difference  as  regards  the  refraction  of  the  other  meridians 
until  you  test  them. 

We  will  have  the  same  results  in  compound  myopic 
astigmatism,  by  using  concave  spherical  glasses  ;  only 
remember  to  use  the  weakest  concave  glass  which  will  stop 
the  movements  in  an  opposite  direction.  Then  calculate 
the  difference,  to  find  the  amount  of  astigmatic  error  of 
refraction. 

In  simple  astigmatism,  with  the  movements  only  in 
6ne  direction,  either  hypermetropic  or  myopic,  you  will 
notice  that  the  convex  or  the  concave  glass  will  cause  the 
movements  to  change  in  the  emmetropic  meridian.  Then 
measure  the  astigmatic  error  as  directed  for  simple  error 
of  refraction,  but  only  noting  the  movements  in  the 
ametropic  meridian. 

These  movements  of  the  retinal  reflex  are  very  inter- 
esting, when  the  astigmatic  error  is  at  any  other  meridian 
than  that  of  the  vertical  or  the  horizontal.  As,  though  you 


RE  TINOSCOP  Y. 


193 


may  rotate  the  mirror  on  the  vertical  or  horizontal  axis, 
yet  you  will  find  that  the  movements  of  the  reflex  will 
always  be  in  the  astigmatic  meridian.  If  the  ametropic 
meridian  be  at  an  angle  of  45  °  from  the  horizontal,  then, 
as  you  rotate  the  mirror  on  the  horizontal  axis,  causing 
the  cylinder  of  light  projected  by  the  plane  mirror  to 
move  up  and  down,  the  movements  of  the  reflex  and 
shadow  will  be  solely  in  the  direction  of  the  astigmatic 
meridian.  So  that  the  moment  you  illuminate  the  eye 


PIG.  87. — DIAGRAM  SHOWING  APPARENT  DIRECTION  OF  THE  RETINAL  REFLEX  m 

ASTIGMATISM  AT  45  °. 

and  move  the  mirror,  you  can  make  your  diagnosis  of 
the  astigmatism.  This  you  will  proceed  to  correct,  in  the 
two  principal  meridians,  the  same  as  if  they  were  vertical 
and  horizontal,  using  the  strongest  convex  and  the  weakest 
concave  glasses. 

Burnett  in  his  "  Treatise  on  Astigmatism"  explains 
this  by  stating  that  in  astigmatism  the  shape  of  the  circles 
of  diffusion,  formed  on  the  retina  by  the  illumination,  is 


194      LECTURES  ON  THE  ERRORS  OF  REFRACT/ON. 

not  round  as  in  simple  refraction,  but  oval,  with  the  long- 
diameter  in  the  direction  of  one  of  the  principal  meridians. 
Then  as  this  oval  moves  across  the  retina,  followed  by 
the  shadowy  edge,  it  seems  to  move  in  the  direction  of 
the  astigmatic  meridian. 

"  Take  a  circular  opening,  as  shown  by  the  circle,  and 
place  behind  it  an  object  with  a  straight  edge  ac,  at  an 
angle  of  45  °,  now  advance  this  object  in  a  strictly  hori- 
zontal direction  to  bdt  the  apparent  movement  of  the 
object  will  be,  not  from  a  to  b,  and  c  to  d,  but  in  the  direc- 
tion of  the  line  ef,  perpendicular  to  ac." 

As  a  means  of  confirming  my  diagnosis  of  refraction 
with  the  test  glasses,  I  have  been  well  satisfied  with  the 
results  obtained  by  the  method  of  retinoscopy  with  the 
plane  mirror,  and  now  use  it  in  all  cases  to  confirm  the  ex- 
aminations. Also  in  the  examination  of  illiterate  persons, 
young  children,  and  those  with  whom  we  cannot  use  the 
other  tests,  you  will  find  this  very  serviceable.  Lastly,  I 
would  advise  you  that  in  the  high  degrees  of  refraction, 
particularly  in  myopia,  if  you  cannot  readily  see  the  reflex 
at  the  distance  of  40  inches,  it  will  only  be  necessary 
for  the  examiner  to  move  to  a  nearer  point,  until  he  can 
readily  appreciate  the  movements  of  the  retinal  reflex. 
You  will  then  proceed  with  the  glasses  placed  before  the 
examined  eye.  In  these  high  degrees  of  ametropia,  the 
emergent  rays  are  so  convergent  or  divergent,  as  the  case 
may  be,  that,  when  they  approach  the  examiner's  eye,  they 
are  so  scattered  that  but  few  will  enter,  and  so  the  image 
formed  on  his  retina  will  be  very  indistinct  at  the  usual 
distance. 


TENTH    LECTURE. 

PRESBYOPIA. 

History — Definition — Causes — Influence  of  refraction  on — Recession  of  near  point — 
Manner  of  testing,  in  the  emmetrope — In  the  hypermetrope — Bifocal  and  Franklin 
lenses — In  myopia — In  astigmatism — Second  sight — Calculation  of  combined  glasses 
— In  anisometropia. 

GENTLEMEN  : — The  time  when  glasses  were  first  used 
for  the  improvement  of  vision  dates  back  more  than  six 
hundred  years.  At  that  time  they  were  used  to  im- 
prove the  vision  of  old  age, — a  condition  which  we  call 
presbyopia. 

The  history  of  the  discovery  and  application  of  the 
lens  to  the  improvement  of  vision  is  very  interesting. 
WALTER  ALDEN,  in  his  book  on  "  The  Human  Eye," 
tells  us  that  even  at  the  excavations  of  the  ruins  of 
ancient  Nineveh  a  "  rock  crystal  lens  "  was  found,  and 
that  in  those  days  the  people  must  have  been  familiar 
with  the  refraction  of  the  rays  of  light  by  a  lens.  He 
says :  "  How  could  men  attain  such  perfection  in  the 
other  branches  of  mathematics,  mechanics,  etc.,  and  yet 
leave  the  subject  untouched,  which  each  drop  of  dew 
sparkling  in  the  sunlight  of  the  morning  would  suggest?" 

Referring  again  to  Alden's  history,  we  go  back  to  the 
days  of  Roger  Bacon,  when  he  occupied  the  chair  of  phi- 
losophy at  Oxford.  He  obtained  some  fine  glass  from 
Belgium,  and  with  this  he  made  some  spectacles  by  grind- 
ing and  polishing  the  lenses  himself,  and  then  imparted 
the  secret  to  his  friends.  COOPER  speaks  of  their  having 
been  worn  by  Henri  Goethals  when  he  was  sixty  years  of 

195 


196  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

age, — glasses  that  had  been  given  to  him  by  his  friend, 
Roger  Bacon,  before  1286.  They  were  carefully  pre- 
served in  those  times,  and  Charles  V.,  after  his  death  in 
1558,  left  among  his  valuables  twenty-seven  pairs  of 
spectacles. 

That  they  were  valuable  there  is  no  doubt,  and  we 
often  wonder  what  people  did  without  them  ;  but,  as 
there  were  so  few  books  at  that  time,  the  necessity  for 
artificial  aid  to  the  normal  eye  was  not  felt  as  at  the 
present  time.  Now  they  are  a  comfort  and  an  assist- 
ance to  almost  every  home  ;  "  for  it  is  not  too  much  to 
say  that  through  the  aid  of  spectacles  we  continue  in  the 
enjoyment,  even  in  old  age,  of  one  of  the  most  noble  and 
valuable  of  our  senses.  They  enable  the  mechanic  to 
continue  his  labors,  and  the  artist  to  display  his  skill  in 
the  evening  of  life  ;  the  scholar  pursues  his  studies  by 
their  help,  adding  to  the  knowledge  of  others,  and  recreat- 
ing his  own  mind  with  intellectual  pleasures,  thus  passing 
days  and  years  in  satisfactory  occupation  that  mi^ht 
otherwise  have  been  devoured  by  melancholy,  or  wasted 
in  profitless  idleness." 

In  the  history  of  spectacles  we  find  that  they  were 
used  for  the  relief  of  the  vision  of  old  age,  to  assist  in  the 
power  to  see  clearly  at  near  points,  and  that  they  have 
continued  to  the  present  day  to  be  of  assistance  to  us 
when  this  condition  of  presbyopia  is  felt  in  the  daily  occu- 
pations of  life. 

Presbyopia^  you  will  find,  commences  generally  in  per- 
sons about  forty  years  of  age.  It  is  first  noticed  by  a 
recession  of  the  near  point,  or,  as  the  patient  will  tell 
you,  he  is  compelled  to  hold  his  morning  paper  almost  at 
arm's  length  to  make  the  vision  clear  and  distinct. 

Donders,  in  his  classical  work  on  Refraction,  (page  210), 
gives  this  definition  of  presbyopia  :  "  The  term  presby- 
opia is  therefore  to  be  restricted  to  the  condition  in  which 


PRESBYOPIA.  197 

as  the  result  of  the  increase  of  years  the  range  of  accom- 
modation is  diminished  and  the  vision  of  near  objects  is 
interfered  with  ; "  and  for  its  correction  requires  a  convex 
glass  of  suitable  focal  power. 

Let  us  now  see  why  this  range  of  accommodation  is 
diminished,  and  why  the  near  point  recedes  from  the  eye. 

I  do  not  consider  this  condition  of  refraction  by  any 
means  abnormal,  but  simply  the  result  of  old  age,  just  as 
gray  hairs  and  other  evidences  appear  in  their  proper 
time,  to  show  that  we  are  gradually  advancing  in  years. 
We  will  therefore  consider  presbyopia  as  a  normal  condi- 
tion of  the  eye  which  all  must  look  for  ;  that  it  will  be  in- 
fluenced according  to  the  refractive  condition  ;  and  that  it 
is  due  partly  to  changes  in  the  curvature  of  the  lens  and 
loss  of  elasticity,  but  chiefly  to  insufficiency  of  the  power 
of  the  ciliary  muscle. 

Presbyopia,  in  all  cases,  will  vary  according  to  the  re- 
fractive condition  of  the  eye.  Hypermetropia  will  cause 
this  recession  of  the  near  point  to  appear  early  in  life, 
while  in  low  degrees  of  myopia  presbyopia  will  appear 
much  later.  You  will  also  find  that  the  state  of  the  gen- 
eral health  will  frequently  have  a  decided  influence  on  the 
appearance  of  this  condition. 

For  these  reasons  you  will  understand  that  we  cannot 
lay  down  any  rules  or  tables  that  will  be  of  any  practical 
value,  except  one  :  that  you  must  test  each  case  separately 
and  carefully  according  to  the  condition  of  the  refraction. 

If  we  consider  presbyopia  in  the  emmetropic  eye,  and 
knowing  that  it  depends  on  the  recession  of  the  near 
point,  you -will  then  find  that  this  point  begins  to  re- 
cede very  early  in  life,  perhaps  about  the  age  of  ten 
years  ;  but  at  that  time  it  is  still  so  near  the  eye  that  the 
gradual  recession  does  not  make  any  difference  in  our 
comfort,  nor  does  the  work  of  the  eyes  cause  any  symp- 
toms of  asthenopia. 


198 


LECTl'KI-.S   0.\'  THE   AA'A'OA'S   OF  KEFR  ACTION. 


At  what  point  on  the  visual  line,  as  this  near  point  re- 
cedes, shall  we  mark  the  place  where  presbyopia  begins  ? 
This  question  must  be  answered  more  from  experience 
than  from  any  positive  facts.  We  find  that  when  the  near 
point  recedes  beyond  8  or  9  inches,  then  the  presbyope 
finds  that  reading  is  not  so  comfortable,  and  they  feel 
the  desire  to  remove  the  paper  or  work  from  the  eyes. 


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FIG.  88. — DIAGRAM  OF  ACCOMMODATION.     (BONDERS.) 

Showing  the  course  of  accommodation  in  an  emmetropic  eye.  The  figures  at  the  top 
of  the  diagram  indicate  the  age,  those  at  the  side  the  amount  of  accommodation, 
and  the  P.P.  in  centimetres  ;  the  oblique  line  represents  the  course  of  the  punctum 
proximum,  and  the  horizontal  line  that  of  the  punctum  remotum  :  the  space  be- 
tween the  two  lines  gives  the  amplitude  of  accommodation.  From  this  diagram  we 
can  calculate  the  amplitude  of  accommodation  possessed  at  any  age.  (Ilartridge.) 

We  say,  then,  that  presbyopia  begins  when  the  near 
point  has  receded  beyond  8  or  9  inches  (216  mm.)  from 
the  eye.  As  it  passes  that  point  and  the  symptoms  of  dis- 
comfort and  fatigue  present  themselves,  we  must  simply 
bring  the  near  point  back  again  within  this  arbitrary 
point,  by  the  use  of  convex  glasses. 

In  the  emmetropic  eye,  under  the  usual  conditions  of 
health,  we  find  that  they  require  about  -\-  .$  D  for  each 


PRE  SB  YOPIA .  1 99 

additional  five  years  beyond  forty.  As  between  40  and  45 
years,  they  require  +  .50,  between  45  and  50  years,  -f- 
i  D,  and  so  on.  I  think  you  will  find  this  rule  nearly 
correct  ;  but,  in  practice,  very  few  emmetropes  consult  an 
oculist — as  regards  their  presbyopia, — but  will  find  glasses 
to  suit  themselves  at  the  optician's.  It  is  therefore  after  they 
have  tried  various  glasses,  without  satisfaction,  that  they 
will  come  to  you  for  relief. 

If  I  would  give  you  a  rule  in  the  selection  of  glasses  for 
presbyopia,  in  the  emmetropic  eye,  I  would  say  :  Test 
each  eye  separately  at  20  feet  and,  finding  V  =  |^,  you 
may  then  order  that  convex  glass  which  will  enable  them  to 
read  No.  r  Jaeger  s  test-type  at  8  or  9  inches  with  com- 
fort. Some  of  our  patients  cannot  see  the  necessity  of 
reading  the  brilliant  type  at  a  point  so  near  the  eyes  ;  but 
it  is  very  obvious  that  if  in  the  normal  eye,  we  enable  a 
person  to  read  at  that  distance,  he  can  easily  and  with 
comfort  read  at  a  point  farther  removed  to  suit  himself. 

Presbyopia,  in  the  normal  eye,  will  require  but  little 
thought  or  judgment.  We  might  consider  it  the  primary 
part  of  the  correction  of  the  errors  of  refraction  ;  but  you 
will  seldom  be  called  upon  to  assist  this  insufficiency  of  the 
ciliary  muscle,  as  it  is  so  seldom  that  the  aid  of  the  oculist 
is  needed. 

What,  then,  does  this  condition  of  presbyopia  imply  ? 
Simply  that  there  is  a  weakening  or  failure  of  the  power 
of  the  ciliary  muscle  to  contract  when  objects  or  letters 
are  brought  near  to  the  eyes,  as  the  entering  rays  of 
light  are  so  divergent  that  the  contraction  of  the  ciliary 
muscle,  by  its  action  on  the  curvature  of  the  lens,  is  not 
sufficient  to  cause  these  divergent  rays  to  focus  upon  the 
retina.  Then,  as  the  presbyope  becomes  older,  we  find 
another  factor  that  will  interfere  with  vision  at  near 
distances — that  is,  a  loss  in  the  elasticity  of  the  lens  ;  so 
that,  though  the  ciliary  muscle  may  contract,  yet  the  lens 


2OO  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

is  not  sufficiently  elastic  to  accommodate  itself  to  the 
relaxation  of  the  capsule.  It  will  retain  almost  the  same 
curvature  as  when  at  rest,  consequently  in  theemmetropic 
eye,  it  is  only  adapted  for  parallel  rays. 

We  may  then  conclude  that  there  is  no  change  in  the 
construction  or  the  formation  of  the  eyeball  as  we 
advance  in  life.  The  eye  is  still  adapted  for  normal  or 
parallel  rays  of  light,  when  at  rest,  but  simply  that  its 
region  of  accommodation  is  reduced  by  a  recession  of  the 
near  point,  the  eye  being  unable  to  adjust  the  refractive 
apparatus  to  vision  for  near  objects. 

Many  presbyopes,  however,  will  seek  your  aid.  Their 
glasses  did  suit  them  at  one  time,  but  are  not  satis- 
factory now  ;  or,  if  suitable,  they  cannot  read  as  long  or 
as  steadily  as  before.  This  may  occur  in  the  emmetropic 
eye,  but  in  that  case  the  patient  simply  needs  a  stronger 
convex  glass  ;  for  you  will  find  that  even  with  the  glasses 
the  near  point  has  receded  beyond  the  limit,  requiring  a 
stronger  glass  to  enable  him  to  read  at  8  or  9  inches. 

But  the  cases  that  will  require  your  attention  are  those 
in  which  we  have  an  existing  error  of  refraction.  Perhaps 
they  have  worn  glasses  for  several  years,  and  now,  passing 
on  to  that  age  when  presbyopia  appears,  they  find  that 
the  glasses  must  be  changed. 

As  hypermetropia  is  the  predominant  error  of  refrac- 
tion, so  will  it  complicate  your  cases  of  presbyopia.  Simple 
hypermetropia  causes  the  condition  of  presbyopia  to 
commence  much  earlier  than  in  the  emmetropic  eye  ;  as,  if 
the  patient  has  been  able  to  overcome  the  hypermetropia 
while  the  lens  was  soft  and  elastic,  yet,  as  time  goes  on,  the 
near  point  recedes  with  him  much  sooner  than  with  the 
emmetrope,  and  he  will  require  a  weak  convex  glass  for 
reading  at  night,  before  he  is  forty  years  old.  Such  a  pa- 
tient as  he  becomes  older,  say  fifty-five  years  or  more, 
will  now  require  glasses  to  assist  his  Hypermetropia.  He 


PRESB  YOPIA .  2O I 

cannot  now  focus  the  parallel  rays  upon  the  retina,  and 
consequently  will  require  glasses  for  distant  as  well  as  for 
near  vision. 

How,  then,  shall  we  test  such  a  case  ?  You  will  first  cor- 
rect the  absolute  hypermetropia,  by  using  that  convex  glass 
which  will  bring  the  distant  vision  to  -f-jj-,  and  with  this 
glass  you  will  see  at  what  distance  he  can  read  the  finest 
type,  as  No.  i  Jaeger.  Then,  if  the  near  point  has  re- 
ceded from  the  eyes  beyond  9  inches,  you  will  add 
to  this  glass  another  convex  glass  to  bring  the  near 
point  within  8  or  9  inches.  The  sum  of  these  two  glasses 
combined  will  give  the  amount  of  presbyopia,  and  the 
glasses  needed  for  reading ;  while,  if  necessary,  the 
glasses  which  neutralize  the  existing  hypermetropia  may 
be  ordered  to  be  worn  constantly  ;  except  when  reading. 
If  your  patient  does  not  wish  to  be  constantly  changing 
the  glasses,  as  the  eyes  are  used  for  near  or  distant  vision, 
you  may  order  them  made  bifocal.  The  glasses  that  have 
the  upper  part  of  the  glass  cut  from  the  lens  required  for 
distant  vision,  and  the  lower  part  from  the  reading  glasses, 
are  called  the  FRANKLIN  lenses  ;  or  you  may  have  both  foci 
ground  on  one  lens — the  upper  part  for  the  distant  vision 
and  the  lower  for  reading.  These  are  called  bifocal  lenses. 

Presbyopia  also  comes  to  those  who  are  myopic,  but 
now  the  myopia  influences  the  presbyopia,  so  that  the 
recession  of  the  near  point  does  not  occur  until  much 
later  in  life.  In  very  high  degrees  of  myopia,  where  the 
far  point  lies  at  or  nearer  to  the  patient  than  8  inches, 
presbyopia  will  never  occur ;  but,  as  I  will  explain  to  you, 
he  will  need  your  advice  in  the  selection  of  glasses  when 
he  feels  the  strain  of  the  ciliary  muscles. 

Let  us  first  consider  those  myopes  of  about  -fa,  or  2  D, 
when  they  use  glasses  only  to  improve  their  distant 
vision.  At  fifty  they  will  begin  to  feel  the  necessity  for 
some  assistance  when  reading,  and  you  will  find  the  near 


202  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

point  has  receded  beyond  8  inches.  A  weak  convex  glass 
that  will  enable  them  to  read  at  a  suitable  near  point 
will  be  all  that  is  necessary  to  relieve  their  presbyopia, 
while  they  will  continue  to  wear  the  concave  glasses  for 
distant  vision. 

Again,  take  the  myope  of  5  to  8  D,  and,  though  in  time 
his  near  point  will  become  the  same  as  his  far  point,  yet 
you  will  find  that  he  cannot  read  with  his  glasses.  They 
will  make  the  rays  of  light  too  divergent.  Now  we  want 
the  effect  of  a  convex  glass,  which  we  obtain  by  ordering 
a  weaker  concave  glass,  so  that  he  can  read  at  about  10 
inches  with  comfort. 

In  those  cases  where  you  have  the  refraction  compli- 
cated with  astigmatism,  it  is  more  difficult  to  fit  them  cor- 
rectly ;  but,  as  we  fit  each  meridian  at  the  distant  point, 
so  must  we  fit  them  for  the  near  point. 

In  presbyopia  complicated  with  astigmatism  of  any 
degree,  simply  remember  to  find  the  two  principal  me- 
ridians ;  then  fit  each  meridian  as  if  the  entire  refraction 
was  of  the  same  degree,  as  in  using  spherical  glasses. 
After  you  have  corrected  the  refraction  for  the  distant 
vision,  you  will  add  to  these  glasses  suitable  convex 
glasses  which  will  make  the  vision  perfect  and  comfortable 
at  the  near  point. 

Let  us  consider,  first,  a  case  of  simple  or  compound 
hypermetropic  astigmatism,  that  has  been  wearing  glasses 
for  several  years.  We  will  find  the  amount  of  hyperme- 
tropic astigmatism,  by  the  trial  with  glasses  at  infinity, 
and  with  this  glass  test  the  power  to  read  No.  i  Jaeger 
at  the  nearest  point.  If  you  find  this  is  beyond  8  inches, 
such  case  has  become  presbyopic  and  will  need,  combined 
with  the  distant  glasses,  a  convex  spherical  glass  that  will 
bring  the  near  point  up  to  8  inches. 

A  still  more  interesting  class  of  cases  are  those  of 
myopic  astigmatism,  particularly  the  simple  forms,  in 


PRESBYOPIA.  203 

which  you  have  one  meridian  myopic  and  the  other  emme- 
tropic.  Now,  if  we  take  each  meridian  separately,  we 
find  that  in  the  myopic  meridian  they  will  not  need  a 
convex  glass,  as  the  refraction  in  that  meridian  is  adapted 
for  divergent  rays,  coming  from  the  near  point  ;  but,  in 
the  opposite  meridian,  being  emmetropic,  they  will  re- 
quire about  the  same  convex  glass  as  the  normal  emme- 
trope  of  the  same  age. 

We  can  illustrate  this  with  a  case  of  simple  myopic 
astigmatism  of  yL,  or  more  fully  expressed,  V  =  -f^,  w. 
"  rV  >  cyl-  ax*s  9°°  ~  IIP  Consequently  we  have  myopia 
of  T]¥  ;  in  the  horizontal  meridian,  and  emmetropia  in  the 
vertical  meridian.  Now,  if  our  patient  be  about  fifty  years 
of  age,  and  his  power  of  accommodation  normal,  he  would 
require  a  glass  of  about  i.  D  focal  distance.  As  he  is  em- 
metropic in  the  vertical  meridian,  so  he  would  require  a 
convex  cylindric  glass  of  i.  D  for  this  meridian,  with  the 
axis  of  the  glass  placed  horizontally  ;  while,  for  the 
myopic  meridian,  as  it  is  adapted  for  divergent  rays  com- 
ing from  a  point  10  inches  in  front  of  the  eye,  conse- 
quently at  the  near  point  of  8  inches,  only  the  slightest 
effort  of  the  accommodation  is  needed  to  assist  the  pres- 
byopia. We  will  therefore  order  for  the  distant  vision 
the  above  simple  concave  cylindric  glass  (— -  y1^-),  with  the 
axis  placed  vertical,  and  for  the  reading  distance  a  simple 
convex  cylindric  glass  (+  -^),  with  the  axis  placed  hori- 
zontal. 

You  must  make  the  same  calculations  in  cases  of  com- 
pound myopic  astigmatism,  only  remember  that  the 
greater  the  amount  of  myopia  the  weaker  the  convex 
glass  required,  according  to  the  age  and  bodily  condition 
of  your  patient. 

Before  closing  this  lecture  on  presbyopia,  I  wish  to 
speak  to  you  of  those  remarkable  cases  of  the  recovery  of 
the  sight  at  a  very  advanced  age,  and  called  second  sight. 


204  LECTURES  OAr  THE  ERKORS  OF  REFRACTION. 

I  know  that  some  persons  are  favored  with  such  remark- 
able power  of  the  ciliary  muscle,  that,  though  they  may 
be  hypermetropic,  yet  they  will  not  need  glasses  until  after 
fifty  or  more  years  of  age  ;  but,  when  you  hear  of  a  case 
where  the  reading  power  has  seemingly  returned  after  the 
age  of  about  seventy  years,  you  may  be  satisfied  of  about 
two  conditions  as  the  cause  of  this  remarkable  sight.  If  the 
case  had  a  thorough  examination,  you  would  either  find 
myopia,  in  which  they  never  saw  well  at  a  distance ;  or 
there  has  occurred  a  slight  swelling  of  the  crystalline  lens, 
due  to  commencing  cataract,  without  perhaps  any  opacity 
of  the  lens  substance.  This  condition  would  act  on  the 
divergent  rays  of  light,  as  if  a  convex  lens  had  been 
placed  before  the  eye.  You  will  at  once  see  that  the 
power  of  the  ciliary  muscles  have  not  returned,  but  that  a 
true  pathological  process  is  no  doubt  taking  place. 

You  must  in  all  cases  first  find  the  actual  condition  of 
the  refraction  ;  find  out  if  there  be  any  existing  error,  either 
hypermetropic,  myopic,  or  any  of  the  various  conditions 
of  astigmatism,  and  correct  fully  and  exactly  with  a 
suitable  glass.  Then  placing  these  glasses  in  your  frame, 
— no  matter  what  may  be  the  combination, — place  the 
glasses  before  the  eyes  and  test  their  region  of  accommo- 
dation, finding  the  near  and  the  distant  point  for  reading 
easily  No  i  Jaeger  test-type.  If  you  find  that  the  near 
point  has  receded  from  the  eyes,  to  a  point  beyond  8  or  9 
inches,  you  should  then  add  convex  spherical  glasses  until 
they  can  read  the  finest  type  at  8  inches,  and  then 
calculate  what  glasses  are  required.  This  would  be  very 
simple  if  you  have  only  used  convex  glasses  for  the  dis- 
tant vision,  where  you  have  hypermetropia  or  hyperme- 
tropic astigmatism.  But  if  you  have  myopia,  though  you 
follow  the  same  process  of  testing  the  vision,  yet  your 
calculations  become  somewhat  more  complicated. 

Let  me  illustrate  this  to  you  by  the  following  case, 


PRESBYOPIA.  205 

both  eyes  being  the  same  as  V  =  -£fa,  w.  -  -  j-g- O  ~~TO"> 
cyl.  ax.  90°  =  |f  ;  patient's  age  fifty-five  years.  Now  with 
this  glass  he  reads  No.  i  Jaeger  at  12  to  20  inches,  then  his 
near  point  has  receded  beyond  the  point  where  presbyopia 
begins.  We  now  add  a  convex  spherical  glass  of  ^,  and 
he  can  easily  read  the  finest  type  at  8  inches.  What 
glasses  shall  we  order  for  this  case  ?  Let  us  make  our 
calculations  in  each  meridian  separately,  and  we  find  in 
the  vertical  meridian  for  distance  -  -  TL,  to  which  we  add 
-j-  ^  then  (—  TV)  -  -  (+  ¥V)  =  -  Ti>*  for  the  vertical 
meridian. 

In  a  horizontal  meridian  we  have  ( — y o")  +  ( — ^V)" 
K=  -  -  -g-1^  then  add  the  convex  spherical  and  we  have 
( —  -g1^)  -  -  (-{-  4*0)  =  -  -  -J-  for  the  horizontal  meridian. 
The  glass  to  be  ordered  is  -  -  y1^  (^  —  ^L,  cyl.  ax.  90  °, 
for  each  eye.  The  cylindric  glass  being  the  same,  and  the 
spherical  glass  reduced,  according  to  the  strength  of  the 
convex  glass  required  to  take  the  place  of  the  weakness 
in  power  of  the  ciliary  muscles. 

You  may  make  this  calculation  much  easier  by  using 
the  metric  system  of  numbering  the  glasses  ;  as  in  the 
vertical  meridian  you  have  -  -  4  D,  and  in  the  horizontal 
meridian  —  6  D,  you  simply  take  i  D  from  each  merid- 
ian, and  we  have  --3  D^)--2  D,  cyl.  ax.  90  °. 

Where  you  have  the  condition  of  anisometropia,  or  a 
difference  in  the  refraction  of  each  eye,  this  method  will 
assist  you  very  much,  as  you  will  then  fit  each  eye  sepa- 
rately and  accurately  for  the  distant  vision,  and,  placing 
these  glasses  before  the  eyes,  test  them  for  the  near 
point.  Add  your  convex  spherical  glass  which  will  bring 
the  near  point  back  to  8  inches,  then  make  your  cal- 
culations for  each  eye  separately,  and  you  will  have  a 
glass  that,  in  the  large  majority  of  cases,  will  be  suitable, 
and  will  correct  their  presbyopia. 

You  may  also  meet  with  some  cases  in  which  there  may 


2O6  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

be  amblyopia,  and  they  cannot  read  the  finest  type  with  any 
glass.  In  such  cases  you  must  ascertain  the  finest  type  which 
they  can  read,  and  using  that  as  your  test,  find  the  nearest 
point,  and  if  this  be  beyond  8  inches,  you  will  use  the 
convex  glass  that  will  bring  their  vision  within  the  proper 
distance.  While,  should  your  case  be  so  illiterate  that 
he  cannot  read — and  we  meet  many  such  cases  in  clinical 
work, — then  find  out  for  what  kind  of  work  he  needs 
glasses,  and  give  him  the  convex  glass  with  which  he  can 
do  that  work  clearly. 


ELEVENTH    LECTURE. 

ILLUSTRATIVE    CASES. 
FROM    PRIVATE    AND    CLINICAL    PRACTICE. 

GENTLEMEN  : — I  have  endeavored  to  explain  the  differ- 
ent methods  of  examination  of  the  eye  for  various  errors 
of  refraction,  and  the  theory  by  which  our  results  are 
obtained.  We  will  now  pass  on  to  the  application  of  the 
practical  work  to  your  patients  by  illustrated  cases  of  the 
different  errors  which  I  have  met  in  private  or  hospital 
practice,  selecting  those  that  will  show  you  the  different 
methods  by  which  we  arrive  at  our  diagnosis,  and  the 
reasons  why  I  should  order  certain  glasses  for  general  or 
special  use. 

I  will  not  advise  you  to  particularly  notice  the  contour 
of  the  head  or  face,  nor  the  length  of  the  eyeball  ;  for 
though  these  various  conditions  may  be  associated  with 
certain  conditions  of  the  refraction — as  asymmetry  of  the 
face  or  head  may  denote  astigmatism,  while  prominence 
or  flatness  of  the  eyeballs  may  denote  myopia  or  hyper- 
opia  respectively — still  in  all  cases  you  must  depend 
primarily  upon  your  careful  test  with  the  glasses  and  the 
confirmation  of  the  result  by  the  retinoscopic  test  and 
the  ophthalmoscope. 

If  we  study  these  cases  in  their  relative  frequency,  I 
find  from  a  reference  to  my  statistics  of  the  refraction  of 
over  1,000  eyes  examined  by  myself,  Dr.  W.  H.  Fox,  and 
Dr.  G.  H.  Bull,  at  the  refraction  room  of  the  Manhattan 
Eye  and  Ear  Hospital,  during  1884  to  1886,  there  were  : 

207 


2O8  LECTURES   O^7  THE    ERRORS   OF  REFRACTION. 

683  cases  hypermetropia, 

1 08  myopia, 

95  "  hyperopia  with  hypermetropic  astigmatism, 

60  "  simple  hyperopic  astigmatism, 

41  "  compound  myopic  astigmatism, 

31  "  mixed  astigmatism, 

28  "  simple  myopic  astigmatism, 

while  but  very  few  were  found  to  be  emmetropic. 

These  results  do  not  agree  with  a  monograph  by  C. 
R.  Agnew,  M.D.,  on  "A  Preliminary  Analysis  of  Ten 
Hundred  and  Sixty  Cases  of  Asthenopia,"  from  the 
report  of  the  Fifth  International  Ophthalmological  Con- 
gress, September,  .  1876,  and  issued  in  1877.  In  this 
monograph  more  than  one-fourth  of  the  cases  he  reports 
were  emmetropid.  I  can  only  say  that  my  cases  were  all 
carefully  examined,  most  of  them  under  the  influence  of 
atropine,  and  yet  there  were  very  few  emmetropic  ;  while 
more  than  one-half  were  hypermetropes  of  different  de- 
grees. This  agrees  much  better  with  the  report  of  the 
"  Examination  under  Atropine  of  the  Refractive  State  of 
Eyes  with  Normal  Vision  |$,  and  Which  Had  .\<  \<  r 
Been  Affected  with  Asthenopia  or  Inflammation,"  by 
Prof.  D.  B.  St.  Jokn  Roosa,  in  which  he  found  80  per 
cent,  hypermetropic  and  only  20  per  cent,  emmetropic  of 
the  persons  examined.'  Also  a  monograph  by  the  late 
Dr.  Edward  T.  Ely,  "  On  the  Examination  of  the  Eyes 
of  Very  Young  Children  under  Atropine,"  in  which  he 
found  them  nearly  all  hypermetropic. 

I  think  we  can  conclude  then,  that  the  largest  propor- 
tion of  cases  which  will  present  themselves  for  your  exami- 
nation will  be  hypermetropic,  and  consequently  this 
condition  will  require  our  attention  first.  Your  cases 
will  give  you  a  varying  history  of  their  asthenopia  :  as, 
"  The  sight  blurs  ;  cannot  read,  or  use  the  eyes,  for  any 
length  of  time  ;  the  eyes  feel  strained  ;  they  have  head- 


ILLUSTRATIVE    CASES.  2OQ 

aches,  pain  in  the  eyeballs,"  etc.,  etc.,  and  other  expres- 
sions indicative  of  weakness  and  irritation. 

CASE  I. — Miss  O.,  age  sixteen,  says  she  can  only  study  at  night  for 
half  an  hour,  when  she  has  dull,  throbbing  pain  behind  the  eyeballs. 
The  eyes  feel  very  tired,  and  the  letters  appear  blurred.  Can  see  well 
at  a  distance. 

On  testing  the  vision  with  Snellen's  test  letters,  I  find  : 

RE,  V=  H; 
L  E,  V  =  if 

If  I  now  place  a  very  weak  convex  glass  before  either 
eye  the  vision  is  blurred,  so  there  is  no  manrfest  hyper- 
metropia,  nor  can  there  be  any  myopia,  as  the  vision  is 
not  reduced.  I  therefore  examine  the  eyes  by  retinoscopy, 
and  find  a  slight  amount  of  hypermetropia,  which  is  con- 
firmed by  the  ophthalmoscope,  showing  about  i  D.  She 
was  now  ordered  a  four-grain  solution  of  atropine,  one 
drop  in  each  eye  three  times  a  day  for  three  days — this 
is  the  usual  solution  that  I  use  to  stop  the  action  of  the 
ciliary  muscle  in  accommodation.  At  the  end  of  that 
time  the  eyes  were  again  tested,  and  V  was  found  to  be 
reduced  to  -§$-  in  each  eye.  Placing  now  a  convex  glass 
of  -fa  before  each  eye  separately  V  =  f-2-  +.  Retinoscopy 
and  the  ophthalmoscope  gave  the  same  result  on  exami- 
nation. 

As  the  total  hypermetropia  was  so  small  in  this  case  I 
did  not  advise  her  to  use  glasses,  confining  my  attention 
to  the  general  health,  and  ordered  a  solution  of  sulphate 
of  eserine,  -fa  gr.  to  one  ounce  of  water,  dropped  in  each 
eye  three  times  a  day.  Under  this  treatment  she  was  re- 
lieved of  all  symptoms  of  asthenopia. 

Bonders  does  not  advise  the  use  of  glasses  in  cases  of 
hypermetropia  of  less  than  -fa,  or  i  D.  But  you  may 
meet  with  cases  that  will  not  be  relieved  without  them. 
In  the  above  case,  had  it  been  necessary,  I  should  have 


210  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

ordered  a  convex  glass  of  -fa,  or  .05  D,  for  use  in  reading 
and  sewing. 

CASE  II.  —  Miss  M.,  age  15,  now  at  school.  Four  months  ago 
she  could  not  see  well  at  a  distance  ;  came  on  gradually,  with  a  blur 
before  the  eyes.  She  could  not  study  at  night,  as  the  light  would  hurt 
the  eyes  and  V  became  blurred. 

On  examination  I  found  : 

R  E,  V  =  ffl,  Hm.  &  ; 
L  E,  V  =  1%,  Hm.  Vr. 

The  ophthalmoscopic  examination  shows  about  2  I  ) 
hypermetropia.  Solution  of  atropine  ordered  for  two 
days,  when  the  vision  became  : 


R  E,  V  =  flfc,  w.  +  iV  =  it  ; 
L  E,  V  =  VW,  w.  +  A  =  !i 


showing  a  total  amount  of  hypermetropia  of  about  2  D. 
She  was  now  allowed  to  stop  the  atropine,  and  after  ten 
days,  to  visual  tests  showed  a  manifest  hypermetropia  of 
^  in  each  eye.  These  glasses  were  ordered  for  constant 
use,  and  two  months  after  she  reports  no  symptoms  of 
asthenopia. 

You  will  find  many  cases  similar  to  the  above,  and  in 
young  persons  I  would  advise  the  use  of  atropine  in  all 
cases,  to  prove  the  amount  of  total  hyperopia,  as  well  as 
to  make  your  test  complete  ;  but  in  persons  of  over  forty 
years  I  would  not  advise  you  to  put  them  to  the  incon- 
venience of  the  loss  of  vision  by  atropine.  Nor  is  it 
necessary,  as  at  that  age  the  power  of  the  accommoda- 
tion is  generally  too  low  to  interfere  with  a  proper  and 
satisfactory  test  with  the  trial  glasses. 

You  wHl  notice  from  these  cases  that  it  is  not  neces- 
sary to  test  the  vision  at  the  near  point,  as  regards  the 
ability  to  read  the  finest  type,  provided  the  distant  vision 
be  -|$,  as  the  region  of  accommodation  is  nearly  always 
the  same  as  that  of  the  normal  eye  ;  and  that  the  strongest 


ILLUSTRATIVE   CASES.  211 

convex  glass  they  will  accept,  without  any  blurring  of  the 
vision  at  a  distance,  will  generally  relieve  them  of  the 
strain  of  the  eyes. 

The  next  condition  of  refraction  which  will  require 
our  attention  is  that  of  myopia,  and  when  free  from  any 
pathological  condition  at  the  fundus,  as  a  low  grade  of 
choroiditis,  you  must  order  a  glass  for  the  different  dis- 
tances at  which  distinct  vision  is  desired,  or  according  to 
the  degree  of  myopia.  I  would  give  glasses  for  different 
distances  in  high  degrees,  while  they  will  only  require  a 
glass  for  the  distant  vision  in  low  degrees,  and  for  the 
medium  degrees  you  may  order  the  same  glass  for  near 
and  distant  vision.  Should  your  test  with  the  glass  be 
satisfactory  and  be  confirmed  by  the  ophthalmoscope, 
there  will  be  no  necessity  to  use  atropine. 

For  instance,  let  me  illustrate  this  by  a  patient  who 
simply  complains  of  diminished  distant  vision,  as  follows  : 

R  E,  V  =  ||,  w.  —  &  =  !$;  L  E,  V  =  same  ; 

can  read  No.  i  Jaeger  test-type  at  4  to  24  inches  without 
a  glass.  In  this  case  I  would  only  order  -  --^  for  dis- 
tant vision  only  ;  no  glass  being  needed  for  reading. 

Again,  if  we  find  that  the  vision  in  each  eye  is  as 
follows  : 

R  E,  V  =  iflfr,  w.  --  TV  =  I*  5  L  E,  V  =  same. 
Now  as   the  region   of  accommodation   is   reduced  to  a 

o 

few  inches,  the  patient  cannot  see  clearly  beyond  the  far 
point,  of  ten  inches,  so  we  may  order  this  glass  to  be 
worn  all  the  time,  giving  perfect  vision  at  a  distance,  and 
also  at  the  near  point,  by  the  exercise  of  a  slight  amount 
of  increased  accommodation.  % 

Let  us  again  consider  a  myopic  case  of  a  higher  degree, 
as  follows  : 

R  E,  V  =  sVo,  w.  —  -I  =  f #  ;  L  E,  V  =  same. 
We  may  order  this  glass  for  distant  vision,  but  for  the 


212      LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

near  point  this  glass  will  cause  the  rays  to  be  too  diver- 
gent, with  an  undue  strain  on  the  accommodation.  I 
think  it  best  to  give  them  a  weaker  glass  for  the  nearer 
points  of  vision,  as  I  have  in  one  case  ordered  one  glass 
for  distance,  one  for  music,  and  another  for  the  reading 
distance.  In  the  use  of  these  glasses  for  reading  the 
book  should  be  held  as  far  away  from  the  eyes  as  possible, 
or  as  far  as  will  make  reading  comfortable. 

We  will  now  examine  a  case  that  is  complicated  with 
astigmatism,  as  follows  : 

CASE  III.  —  Miss  Clara  R.,  age  22.  She  has  been  wearing  glasses 
for  several  years,  but  they  are  not  suitable,  nor  do  they  relieve  the 
pain  in  the  eyeballs  ;  has  blurring  of  the  vision  when  reading  ;  has 
slight  blepharitis. 

This  case  will  illustrate  to  us  our  third  largest  per- 
centage of  cases,  from  the  following  examination  : 

R  E,  V  =  Jfr,  w.  +  A,  cyl.  ax.  90°  =  f  |  ; 
L  E,  V  =  if  Hm.  ^,  cyl.  ax.  90°. 

I  found  these  glasses  the  best  at  the  time  after  several 
trials  with  sphericals,  but  the  test  was  not  confirmed  by  the 
ophthalmoscope,  and  I  was  not  satisfied  with  the  result. 
I  ordered  the  solution  of  atropine  three  times  a  day. 
After  three  days  the  result  was  : 


R  E,  V  =  flV,  w.  +  Vi,  C  +  A,  cyl.  ax.  100°  =  f|  ; 
L  E,  V  =  flV,  w.  +  t  C  +  dr,  cyl.  ax.  80°  =  if 

The  ophthalmoscopic  examination  shows  in  the  R  E  +  3 
D  vertical  and  +50  horizontal  ;  L  E,  +  4  D  vertical 
and  +50  horizontal.  After  the  effects  of  the  mydriatic 
had  passed  off,  she  accepts  the  following  glasses  : 

R  B|fV  =  tffr  w.  +  Vff  C  +  -rV,  cyl.  ax.  100°  =  |ft  ; 
L  E,  V  =  ft  w.  +  V*  C  +  A,  cyl.  ax.    80°  -  if 

These  glasses  were  ordered  for  constant  use,  both  for 
distant  and  near  vision.  Several  months  after,  she  re- 
ported to  me  that  the  glasses  had  relieved  her  asthenopia. 


ILLUSTRATIVE    CASES.  213 

In  this  case  you  will  notice  a  certain  amount  of  ambly- 
cpia  in  the  right  eye ;  that  is,  the  vision,  after  correction 
with  the  proper  glasses,  did  not  reach  the  normal  stand- 
ard of  !$,  but  remained  at  |-jj-.  We  frequently  find  this 
condition  when  testing  cases  of  hypermetropia,  as  I  have 
explained  in  the  lecture  on  that  subject.  You  can  only  rec- 
ommend the  glass  that  will  give  the  best  vision  at  the  dis- 
tant point.  By  the  use  of  atropine,  in  this  case,  I  was  able 
to  obtain  the  exact  meridians  of  the  astigmatism,  finding 
it  at  90°  before  the  atropine  was  used  ;  when  under  its 
influence,  the  meridians  at  which  I  could  get  the  best 
vision  were  those  shown  in  the  examination,  changing 
the  inclination  of  the  axis  of  the  cylindric  glass  toward 
each  temple. 

CASE  IV. — Miss  E.,  age  26.  One  year  ago,  after  doing  some  very 
fine  work,  she  had  a  feeling  of  fulness  in  the  left  eye,  with  blurring  of 
the  vision.  This  blurring  has  continued  with  pain  in  and  around  the 
•eyes,  and  lachrymation.  Has  constant  pain  referred  to  the  top  of  the 
head.  She  has  never  worn  glasses. 

On  testing  the  eyes  with  the  trial  glasses,  I  found  this 

result : 

R  E,  V  =  ft  Hm.  ¥V  ; 
L  E,  V  =  ft  Hm.  &. 

As  this  examination  was  not  satisfactory,  while  the  oph- 
thalmoscope showed  a  certain  amount  of  astigmatism,  I 
ordered  atropine,  to  be  used  four  days,  with  the  following 
result : 

R  E,  V  =  ft  w.  +  &,  C  +  &,  cyl.  ax.  80°  =  gft  ; 

L  E,  V  =  ft  w.  +  ^,  C  +  *V,  cyl.  ax.  100°  =  ft 

The  ophthalmoscope  and  the  test  by  retinoscopy  gave  the 
same  results.  She  was  then  tested  with  th*  stenopseic 
slit,  which  placed  at  180°  with  +^,  V  :=  f#,  and  at  90°  with 
_j_  j_;  V  =  f-jj-,  showing  that  in  the  vertical  meridian,  there 
was  a  certain  amount  of  hypermetropia,  and  in  the  hori- 
zontal meridian,  about  i  D.  Now,  the  vertical  meridian 


214  LECTURES   ON  THE   ERRORS   OI-    REER  ACTION. 

was  not  emmetropic,  but  after  the  effects  of  the  atropine 
had  ceased,  she  would  not  accept  any  spherical  glasses,  so 
I  ordered  the  cylindrics  of  the  full  strength  accepted 
when  under  atropine.  She  was  given  this  glass  : 

R  E,  +  ^,  cyl.  ax.  80°  ; 
L  E,  +  ^g,  cyl.  ax.  100°. 

You  may  ask,  How  do  I  decide  that  these  glasses  give  the 
best  vision  ?  Well,  we  know  that  the  patient  cannot  be  my- 
opic, as  the  distant  vision  is  about  normal  and  is  not  made 
worse  by  weak  convex  glasses.  I  first  select  the  strong- 
est convex  glass  which  will  make  any  improvement  in  the 
vision  at  infinity.  Placing  this  before  the  eye,  I  now  try  if 
they  can  see  all  the  lines  clearly  on  the  card-test  for  astig- 
matism (Greens),  and  find  that  the  horizontal  lines  are  most 
distinct.  Placing  a  convex  cylindric  glass  before  the  spheri- 
cal, and  turning  its  axis  from  the  right  to  the  left  until 
all  the  lines  appear  equal,  I  use  then  the  test-letters 
(Snellcns),  and  find  the  strongest  convex  cylindric  which  the 
patient  will  accept.  This  done,  I  now  reduce  the  spherical 
to  see  if  I  have  over-corrected  the  meridian  of  least  ame- 
tropia. 

As  in  this  case  after  the  use  of  atropia,  I  found  that 
she  would  only  accept  the  cylindric  glasses,  the  total 
amount  of  her  hyperopia  being  too  small  to  need  correc- 
tion and  give  satisfactory  vision. 

You  will  again  notice  that  in  these  tests  for  hyperme- 
tropia  I  have  made  no  mention  of  the  near  vision.  Why 
so  ?  Because  I  do  not  consider  it  essential,  as  you  will 
always  find  in  young  persons  the  amplitude  of  accom- 
modation Ts  sufficiently  great  to  give  them  perfect  near 
vision,  their  asthenopia  arising  only  from  the  excess  of 
accommodation  required  at  reading,  etc.  So  that,  if  you 
stop  this  strain,  and  neutralize  their  manifest  hypermetro- 
pia  only,  you  will  relieve  their  asthenopia. 


ILLUSTRATIVE    CASES.  21$ 

In  older  persons,  as  they  have  passed  the  age  of  forty, 
and  presbyopia,  or  old-age  sight,  comes  on,  then  you  must 
test  them  for  their  near  vision,  giving  them  glasses  for 
both  near  and  distant  sight.  Take  any  of  these  four  cases 
that  I  have  recorded,  and,  as  they  become  presbyopic, 
you  will  have  to  add  to  the  glasses  which  correct  their 
refraction  suitable  convex  spherical  glasses  to  bring  the 
near  point  within  the  distance  at  which  they  are  accus- 
tomed to  read. 

I  would  illustrate  this  to  you  as  follows  : 

CASE  V. — Mrs.  S.,  age  40,  has  worn  glasses  for  12  years,  but, 
though  they  relieved  her  at  first,  she  now  has  asthenopia,  with  headache, 
and  to  see  well  at  night  the  eyes  feel  strained. 

I  find  on  examination  and  the  test  with  glasses  that  her 
vision  at  20  feet  is  only  |~{j-,  and  with  a  convex  spherical  of 
-j-gL,  V  =  f -§-  +,  shows  an  absolute  hyperopia  of  more 
than  i  D.  But  with  this  glass  she  can  only  read  No.  2  of 
Jaeger  test-type  at  14  inches,  so  we  must  assist  the  action 
of  accommodation  still  more  by  stronger  convex  glasses. 
Placing  now  -{-  ^  before  each  eye,  or  adding  -}-  -fa  to  the 
glasses  which  correct  her  absolute  hypermetropia,  she  can 
now  read  No.  i  Jaeger  at  8  inches.  I  order  for  her  dis- 
tant vision  -[-  -fa  and  for  her  near  vision  -f  ^V- 

CASE  VI. — Miss  S.  S.  has  always  been  near-sighted,  and  worn 
glasses  for  seven  years,  but  only  for  distant  vision.  When  reading  half 
an  hour,  she  has  pain  in  the  eyes  and  thinks  they  are  getting  worse.  She 
holds  her  book  at  about  8  inches  from  the  eyes.  Never  succeeded  in 
getting  glasses  suitable  to  read  with. 

Her  distant  vision  is  only  ?fa,  and  on  testing  the  eyes 
separately  I  find  the  vision  as  follows : 

R  E,  V  =  ^¥,-w.  —  TV,  V  =  ft 
I  now  add  the  concave  cylindric  and  find  that 

with  TV,  cyl.  ax.  160  °,  V  =  f  #  — . 
So  that  she  has  a  myopia  of  TL,  in  the  meridian  of  160°, 


2l6  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

and  about  \,  in  the  meridian  of  70°,  or  at  right  angles  to 
the  axis  of  the  cylindric  glass. 

L  E,  V  =  rf,,  w.  —  -1,3  —  fa  cyl.  ax.  20  °  =  |f  - 

About  the  same  as  in  the  right  eye,  only  you  will  notice 
that  there  is  a  similar  position  in  reference  to  the  axis  of 
the  cylindric  glasses  ;  the  R  E  being  at  160°  and  the  L 
E  at  the  corresponding  angle  of  20°.  As  these  glasses 
indicate  rather  a  high  degree  of  myopia  in  one  meridian, 
I  examine  her  with  the  other  tests,  as  the  ophthalmoscope, 
retinoscopy,  and  the  stenopaeic  slit,  all  of  which  confirm 
the  result.  But  if  these  tests  do  not  agree,  as  a  part  of  the 
myopia  may  be  due  to  spasm  of  the  ciliary  muscle,  you 
should  then  place  your  patient  under  the  influence  of  a  my- 
driatic.  In  this  case,  to  confirm  my  examination,  and  as 
it  is  advisable  to  do  in  all  cases  of  astigmatism,  I  order 
the  four-grain  solution  of  atropine,  and  on  again  testing 
her  with  the  trial  glasses  I  found  the  same  result. 

Now,  as  the  general  myopia  was  only  y1^, — a  glass  that 
we  can  order  for  near  and  distant  vision, — I  order  these 
compound  glasses  to  be  worn  all  the  time  ;  and  she 
reported  her  glasses  satisfactory,  with  relief  from  her 
headache  and  pain  in  the  eyes  when  reading. 

You  will  find  many  cases  that  will  represent  the  errors 
of  refraction  which  I  have  illustrated,  with  different  degrees 
of  ametropia ;  with  the  axis  of  the  cylindric  glasses  in 
the  different  meridians,  most  of  them  will  be  at  90°,  next 
at  1 80°,  and  the  rest  between  these  two  meridians,  with 
generally  a  symmetrical  relation  in  the  axis  of  the  cylin- 
dric glasses.  But,  should  you  find  the  axis  the  same  in 
both  eyes,  as  45  °  in  each,  I  would  advise  you  to  examine 
them  very  carefully,  to  exclude  all  source  of  error,  and  to 
test  the  near  vision  in  reference  to  the  shape  of  certain 
objects,  as  a  book  or  any  object  with  right  angles. 

There  are  certain  conditions  of  the  refraction  that  may 


ILLUSTRATIVE   CASES.  2 1/ 

be  concealed,  as  the  test  with  the  trial  glasses  will  give  an 
entirely  different  result  from  the  examination  with  the 
ophthalmoscope.  This  can  only  be  due  to  a  change  in 
the  curvature  of  the  lens,  caused  by  the  action  of  the 
ciliary  muscle.  I  will  illustrate  it  to  you  in  this  case  : 

CASE  VII. — Miss  K.,  age  20.  This  patient  has  a  constant  blur- 
ring of  the  vision,  which  she  has  noticed  lately.  Has  occasional  sharp 
pains  in  the  eyes.  She  can  read  for  about  twenty  minutes,  when  the 
eyes  feel  tired.  Thinks  she  is  getting  near-sighted.  This  pain  may  be 
due  to  the  contraction  of  the  ciliary  muscle. 

There  is  no  doubt  that  from  constant  study  persons 
become  near-sighted,  and  this  is  apt  to  take  the  pro- 
gressive form.  (See  myopia.)  But  this  case  presents  a 
train  of  symptoms  too  recent  in  their  history,  while  the 
asthenopia  would  indicate  hypermetropic  refraction.  Let 
us  see  what  the  test  will  show  : 

R  E,  V  =  §i  w.  —  ^,  =  fft  ; 
L  E,  V  =  H,  w.  —  jz,  =  fi 

She  would  not  accept  any  convex  glasses,  as  even  the 
weakest  would  make  the  letters  more  indistinct  ;  but  the 
small  amount  of  apparent  myopia  led  me  to  suspect  a 
different  refraction.  I  then  tested  her  with  the  ophth- 
almoscope and  by  retinoscopy  :  both  tests  indicated  hy- 
permetropia  of  about  i  D.  This  would  indicate  that 
the  refraction  of  the  eyes  must  be  different  when  they  are 
in  active  use  or  when  examined  in  the  dark  room.  I  or- 
dered the  solution  of  atropine  three  times  a  day,  for  five 
days,  with  this  result  on  examination  : 

R  E,  V  =  M,  w.  +  A,  =  I*  ; 
L  E,  V  =  f£,  w.  +  ^V,  =  **• 

This  result  was  fully  confirmed  by  the  other  tests,  and  the 
myopia  had  disappeared. 

If  you  will  remember  the  lecture  on  myopia  and  the 
accommodative  form,  I  endeavored  to  explain  to  you  why 
these  cases  should  present  this  apparent  myopia.  The 


2l8  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

vision  is  at  once  brought  up  to  the  normal  standard  by 
the  convex  glasses  and  the  action  of  atropine.  We  know 
that  this  drug  stops  the  action  of  the  ciliary  muscle, 
and  we  know  that  by  a  spasm  of  the  ciliary  muscle  the 
lens  would  become  more  convex.  This  would  make  the 
refractive  power  much  greater,  and  so  will  focus  the  rays 
of  light  from  infinity  at  a  point  in  front  of  the  retina. 
After  using  the  atropia  for  a  few  days  it  was  discon- 
tinued. At  the  end  of  about  ten  days  the  action  of  the 
accommodation  had  returned,  and  all  evidences  of  the 
myopia  had  disappeared.  She  then  accepted  and  pre- 
ferred the  weak  convex  glasses,  and  I  ordered  -h  -gi^,  for 
each  eye,  to  be  worn  constantly  until  relieved. 

You  will  generally  find  this  condition  associated  with 
hypermetropia  in  young  persons  ;  though  you  may  find 
it  in  the  emmetropic  as  well  as  in  the  myopic  eye.  In 
myopes  it  is  shown  by  their  requiring  a  much  stronger 
concave  glass  than  is  confirmed  by  the  other  tests.  The 
ophthalmoscope  may  only  show  myopia  of  ^,  and  yet 
they  will  require  -  -  -fa,  to  read  |JJ.  In  all  these  cases  of 
suspected  spasm  of  the  accommodation,  you  must  stop  the 
action  of  the  muscle  of  accommodation  by  a  mydriatic,  of 
which  atropine  is  the  best.  If  the  spasm  does  not  yield 
readily  to  the  action  of  the  medicine,  keep  them  under  the 
influence  of  the  drug  until  all  symptoms  of  the  spasm  have 
disappeared. 

These  cases  are  particularly  interesting  in  the  results 
of  your  examinations  and  the  relief  they  will  obtain  by 
wearing  the  proper  glasses  ;  while  a  mistake  in  your  diag- 
nosis and  the  ordering  of  concave  glasses  would  only  tend 
to  increase  the  pain  and  discomfort. 

Another  class  of  cases  that  we  meet,  presenting  some 
symptoms  the  opposite  to  those  of  the  spasm,  is  shown  in 
the  following  case,  where  we  have  the  ciliary  muscle  again 
at  fault : 


ILLUSTRATIVE    CASES.  2IQ 

CASE  VIII. — Master  James  B.,  age  12.  He  has  lately  recovered 
from  an  attack  of  sore-throat  that  was  supposed  to  have  been  diphthe- 
ritic. He  now  complains  that  he  cannot  see  the  black-board  at  school, 
nor  can  he  possibly  see  to  read  at  any  distance. 

The  parents  are  always  very  much  alarmed  at  the  loss 
of  the  sight  in  these  cases  ;  but  you  can  easily  show  them 
with  the  proper  glass  that  the  vision  is  perfect  at  both 
near  and  distant  points.  Let  us  test  this  case  with  the 
glasses,  and  we  find  as  follows  : 

R  E,  V  =  TVo,  w.  +  TV,  -  B  5 
L  E,  V  =  TW,  w.  +  TV,  =  H. 

He  cannot  read  Jaeger's  test-type  at  any  distance  ;  but  if 
we  place  glasses  before  each  eye,  convex,  of  8  inches  focal 
distance,  he  will  readily  read  No.  i  Jaeger,  the  finest  type, 
at  about  10  or  1 1  inches.  With  such  results  there  can  be 
no  fault  at  the  fundus  of  the  eye,  and  the  trouble  must  be 
due  to  deficiency  in  the  action  of  the  muscle  of  accom- 
modation. 

You  will  notice  that  this  case  presents  all  the  evidence 
of  hypermetropia,  under  the  influence  of  atropia  ;  or  the 
condition  of  refraction  which  we  find  in  elderly  persons,  and 
the  power  of  the  ciliary  muscle  is  about  nil.  There  is,  in 
fact,  an  almost  complete  paralysis  of  the  muscle  of  ac- 
commodation. The  pupils  are  slightly  affected,  there 
will  be  slight  dilatation,  and  they  will  respond  but  feebly 
to  the  action  of  light  ;  showing  that  the  ciliary  branches 
of  the  third  nerve  which  supplied  this  muscle  and  the  iris 
were  affected  by  the  action  of  the  diphtheritic  poison. 

How  will  we  treat  these  cases  ?  I  would  not  advise 
you  to  order  glasses  at  first,  but  to  try  the  effects  of  time 
and  the  use  of  a  suitable  tonic  to  the  general  system  ; 
for  which  I  prefer  the  muriate  tincture  of  iron,  10  drops 
three  times  a  day.  If  your  patients  should  beemmetropic, 
or  have  a  slight  degree  of  hyperopia,  they  will  rapidly 
improve  under  the  use  of  the  tonic,  and  the  vision  will  be 


220  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

restored  ;  but  should  they  present  a  high  degree  of  hy- 
permetropia,  as  this  little  patient,  you  may  order  a  glass 
which  will  correct  their  refraction  for  distant  vision,  to  wear 
until  all  symptoms  of  weakness  in  the  muscle  of  accommo- 
dation have  disappeared.  I  would  not  order  glasses  for 
the  reading  distance  unless  necessary,  but  wait  until  the 
eye  has  recovered  the  power  of  accommodation. 

While  speaking  on  the  subject  of  the  loss  of  the  ac- 
commodative power,  let  me  present  to  you  the  following 
case.  This  case  was  reported  by  myself  some  years  ago, 
and  presents  a  rare  condition,  particularly  interesting  as 
regards  the  results  of  the  examination.  It  is  the  only 
case  of  the  kind  in  the  number  that  I  have  examined  in 
the  office  and  at  the  hospital.  I  report  it  in  full,  that  you 
may  appreciate  the  different  methods  by  which  the  eye 
was  examined  : 

CASE  IX. — Mrs.  M.  A.  S.,  age  23,  gave  me  the  following  history. 
She  first  went  to  school  at  the  age  of  seven  years,  and  at  that  time, 
when  studying,  would  always  place  her  books  as  far  away  from  the  eyes 
as  possible,  or  stand  away  from  the  teacher  ;  while  the  other  children 
would  be  at  the  teacher's  knee.  This  continued,  and  as  she  advanced 
in  age,  she  would  sew  and  read  at  arm's  length,  so  that  her  work  would 
be  constantly  slipping  off  her  lap.  She  would  try  to  bring  her  work 
or  book  nearer,  but  vision  would  blur,  and  at  once  she  was  compelled 
to  place  the  work  further  away.  She  never  suffered  from  any  of  the 
acute  diseases  of  childhood,  as  scarlatina  or  diphtheria,  and  only  a 
slight  attack  of  measles  ;  while  since  then  she  has  always  had  good 
health.  The  other  members  of  her  family  have  good  eyesight,  except 
one  sister,  who  has  been  troubled  with  a  medium  degree  of  hyperme- 
tropic  astigmatism  ;  while  her  mother  did  not  become  presbyopic  until 
she  was  over  50  years.  Mrs.  S.  can  read  for  several  hours  without 
material  fatigue,  provided  she  holds  the  book  at  a  distance  of  about 
two  feet  from  the  eyes  ;  and  always  prefers  to  read  in  a  medium  light, 
as  a  bright  light  is  too  dazzling.  She  has  sometimes  felt  slight  attacks 
of  pain,  referred  to  the  balls  of  the  eye,  when  reading  for  several  hours, 
but  did  not  consider  that  she  had  any  particular  trouble  until  she  came 
to  me  with  a  slight  attack  of  catarrhal  conjunctivitis,  that  yielded  read- 
ily to  treatment. 


ILLUSTRATIVE   CASES.  221 

On  ophthalmoscopic  examination  the  fundus  appeared 
perfectly  normal  and  the  media  clear ;  with  a  slight 
amount  of  hypermetropia,  about  i  D.  On  testing  her 
distant  vision  it  was  found  to  be  : 

R  E,  V  =  f£,  Hm.  ¥V  ; 
L  E,  V  =  f  fr,  Hm.  ¥V 

Her  near  point  with  No.  i  Jaeger  was  found  at  20  inches, 
and  the  far  point,  with  the  same  type,  at  30  inches,  in 
each  eye  ;  with  a  slight  blurring  of  the  vision  in  the  right 
eye  when  reading  very  fine  type. 

She  has  homonymous  diplopia  at  a  distance  of  20  feet, 
with  a  prism  of  12°  base  upward,  placed  over  either  eye. 
This  is  corrected  with  a  prism  of  3  °  base  outward.  The 
internal  rectus  can  only  overcome  a  prism  of  8°,  and  the 
strength  of  the  external  rectus  is  represented  by  a  prism 
of  5°. 

The  positive  part  of  her  accommodation  shows  only  -^, 
and  the  negative  part  ^  for  binocular  vision,  with  the  visual 
axes  fixed  at  her  near  point  of  20  inches.  Her  range  or 
power  of  accommodation  is  only  about  -J-g-,  with  a  region  of 
accommodation,  with  No.  i  Jaeger  test-type,  of  10  inches. 
This  exists  only  at  arm's  length,  or  20  to  30  inches  from 
the  eyes. 

She  was  placed  under  a  four-grain  solution  of  atropia 
for  four  days,  instilled  three  times  a  day,  when  the  dis- 
tant vision  in  each  eye  had  fallen  to  f^,  and  with  a  con- 
vex glass  of  36  inches  focal  distance  vision  was  brought 
up  to  normal,  or  -§-[}-  ;  showing  a  total  hypermetropia  in 
each  eye  of  -^. 

In  looking  over  this  history  and  seeking  for  an  ex- 
planation of  the  results  contained  therein,  and  endeavor- 
ing to  arrive  at  a  definite  diagnosis,  we  are  compelled  to 
do  so  by  exclusion,  or  by  the  negative  results.  While  the 
present  symptoms  would  indicate  the  existence  of  a  par- 


222  ZAC'/TAV-.V   OAr  Till-.    I-'.KROKS   OF   KI-.I-'KACTION. 

tial  paralysis  of  the  ciliary  muscle,  we  can  find  no  cause 
in  her  past  history  for  any  such  conclusion,  as  this  condi- 
tion has  existed  since  early  childhood,  when  she  was  not 
afflicted  with  any  disease  to  cause  partial  paralysis. 

I  am  inclined  to  think,  as  we  study  the  various  phe- 
nomena presented  by  this  case,  that  there  is  no  pathologi- 
cal condition  existing  whatever;  that  when  the  visual  axes 
are  fixed  on  ''nfinity,  her  slight  degree  of  hypermetropia  is 
overcome  by  the  action  of  the  ciliary  muscle  and  we  have 
vision  =  |$,  or  normal  ;  but  that,  when  the  vision  is  changed 
to  a  nearer  point  and  divergent  rays  enter  the  eyes,  the 
normal  action  of  the  ciliary  muscle  fails  to  respond,  the 
vision  becomes  blurred,  and  No.  i  Jaeger  test-type  can 
be  seen  only  at  arm's  length,  or  from  20  to  30  inches.  This 
conclusively  shows  that  there  must  be  an  almost  total 
absence  of  any  accommodative  power.  This  is  particularly 
shown  in  the  right  eye,  from  the  fact  that  she  frequently 
complains  of  a  blurring  of  the  vision  in  that  eye,  with 
dilatation  of  the  pupil. 

If  we  compare  the  results  obtained  in  this  case  with 
those  of  the  normal  eye,  both  as  regards  the  extrinsic  and 
intrinsic  muscles  of  the  eyes,  they  will  be  found  below  the 
standard.  The  power  of  the  internal  recti,  as  shown  l>y 
the  test  with  prisms,  is  only  about  one  third  the  strength 
of  the  normal  muscles.  She  can  only  fuse  the  image  of  a 
candle  flame  with  a  prism  of  8°  with  the  base  outward, 
while  the  normal  standard  exists  at  about  25  °  for  the 
internal  rectus. 

I  consider  that  this  weak  condition  of  the  muscles  of 
adduction  is  probably  due  to  the  fact  that  her  near  point 
is  so  far  removed  from  the  eyes  that  the  muscles  have 
had  no  stimulus  to  develop  their  contractile  power  to  the 
normal  strength  and  action. 

As  regards  the  intrinsic  muscle,  or  the  muscle  of  ac- 
commodation, to  all  the  tests  to  which  it  was  subjected  it 


ILLUSTRATIVE    CASES.  22$ 

failed  to  respond.  Comparing  the  positive  and  the  negative 
part  of  the  accommodation,  or  the  relative  range,  and  we 
find  it  only  as  i  to  i  ;  while  in  the  normal  eye  it  should 
be  as  2  to  3.  In  my  eyes,  with  the  visual  axes  fixed  at 
the  same  angle,  the  relative  range  is  about  as  i  to  2. 

You  can  readily  measure  this  relative  range  of  accom- 
modation in  your  eyes  by  placing  No.  i  Jaeger  test-type  at 
a  fixed  point,  say  15  inches,  and  then  placing  the  strongest 
concave  glass  before  each  eye  for  the  positive  part,  and 
the  strongest  convex  glass  for  the  negative  part,  through 
which  you  can  read  the  type  easily.  The  concave  glasses 
will  increase  the  action  of  the  accommodation,  while  the 
convex  glass  will  cause  it  to  relax. 

Also  examine  this  patient's  binocular  range  of  accomo- 
dation,  and  it  falls  to  about  -^  ;  i.  e.  with  a  convex  glass  of 
-^L-  placed  before  each  eye,  would  give  rays  of  light  coming 
from  20  inches,  her  near  point,  as  if  they  came  from  infin- 
ity. This  is  very  far  below  the  normal  range  of  J,  show- 
ing that  the  accommodative  power,  with  the  convergence 
of  the  visual  axes,  is  very  small.  This  is  also  shown  in 
the  region  of  accommodation,  with  No.  i  Jaeger  test-type, 
existing  at  20  to  30  inches  from  the  eyes — a  region  too 
far  removed  and  too  small  to  be  of  any  practical  service 
whatever. 

As  it  is  a  self-evident  fact  that  in  this  case  there  is 
an  almost  entire  absence  of  any  accommodative  power,  it 
would  be  well  to  again  consider,  as  we  have  in  the  previ- 
ous lecture,  what  are  the  essential  elements  concerned  in 
that  act. 

The  normal  'or  emmetropic  eye,  when  all  its  refractive 
elements  are  at  rest,  will  so  bend  rays  of  light  from  in- 
finity that  they  will  exactly  focus  on  the  retina  at  the 
macula  lutea.  They  there  will  produce  an  exact  inverted 
image  of  the  object  to  which  the  visual  axes  are  directed. 
But  as  this  object  is  brought  nearer  to  the  eyes,  the  rays 


224  /./•.V/y/VA.S    ON  THE   EKKOKS   OF  KEFKAC';"/O.\'. 

become  more  and  more  divergent  and  will  focus  behind 
the  retina,  producing  on  that  sensitive  layer  of  nerve 
cells  circles  of  diffusion,  provided  the  refractive  appa- 
ratus remain  at  rest  and  the  refractive  angle  continue 
the  same.  But  the  inherent  faculty  of  the  eyes  will 
abhor  any  blurred  vision,  as  nature  is  said  to  "  abhor 
a  vacuum,"  so,  as  the  object  is  brought  closer  to  the  eyes, 
the  act  of  accommodation  takes  place,  the  eye  adjusts  its 
refractive  power  to  the  vision  at  a  nearer  point,  and  will 
so  bend  the  rays  of  light  that  they  will  exactly  focus  upon 
the  retina. 

To  accomplish  this  act,  the  intrinsic  muscle  of  the 
eye  contracts  (see  Lecture  I.),  whereby  the  zone  of  Zinn  is 
relaxed  and  the  lens  pushes  forward  the  anterior  capsule 
by  its  elasticity.  This  increases  the  refractive  power  so- 
that  it  can  exactly  focus  the  divergent  rays  of  light  that 
proceed  from  an  object  brought  nearer  the  eye. 

But  in  this  case  we  have  a  condition  of  hypermetro- 
pia,  or  congenital  shortening  of  the  eyeballs,  so  that  the 
ciliary  muscle  must  contract  to  focus  parallel  rays  and 
make  distant  vision  perfect.  But  there  its  power  prac- 
tically stops,  and  we  are  compelled  to  conclude  that  the 
fault  must  lie  in  the  diminished  action  of  the  ciliary 
muscle.  I  should  think  that  there  must  be  a  congenital 
deficiency  of  the  circular  fibres  of  that  muscle,  or  a  con- 
dition of  muscular  atrophy  occurring  in  early  childhood. 
Hence  the  only  diagnosis  possible  :  an  almost  total  defi- 
ciency of  the  accommodative  power  of  the  eyes, — probably 
congenital. 

The  only  treatment  for  the  relief  of  this  case  can  be 
by  placing  before  the  eyes  convex  glasses,  so  as  to  bring 
the  near  point  within  a  distance  of  about  lo  or  i  2  inches 
from  the  eyes,  which  on  trial  was  found  to  be  +  -^  .  This 
glass  I  accordingly  ordered  for  each  eye. 

I  have  reported  this  case  to  you  fully,  as  it  presents 


ILLUSTRATIVE   CASES.  22$ 

some  very  interesting  and  instructive  features  for  our 
study,  while  it  is  an  extremely  rare  one.  We  will  now 
proceed  to  study  some  cases  that  present  unusual  features 
in  prescribing  glasses. 

In  prescribing  glasses  for  persons  past  the  age  of  forty 
years,  when  they  become  presbyopic,  you  will  find  this 
condition  frequently  complicated  with  some  of  the  errors 
of  refraction  that  have  existed  before  that  time,  and  which 
must  be  taken  into  consideration.  They  will  require 
very  different  glasses  from  those  usually  ordered  for  the 
-emmetrope.  I  will  illustrate  this  to  you  by  the  following 
cases  : 

CASE  X. — Mr.  S.  M.,  age  50,  has  worn  concave  glasses  for  many 
years,  but  only  to  improve  his  distant  vision.  His  glasses  are  —  £$  for 
each  eye.  He  complains  that  he  cannot  read  comfortably  except  at 
about  20  inches  from  the  eye. 

His  distant  vision  is  found  to  be  f$,  each  eye,  with 
_  ^i_.  There  is  no  increase  in  the  myopia,  but  he  cannot 
read  No.  i  Jaeger  except  in  the  region  of  his  far  point, 
so  that  he  has  very  little  power  in  the  accommodation. 
With  +  -jL  he  readily  reads  No.  i  Jaeger  test-type  at  8 
inches,  so  that  he  will  require  a  convex  glass  (+-?V)  for 
reading,  and  a  concave  glass  ( —  ^¥)  for  his  distant  vision. 
In  the  higher  grades  of  myopia  you  will  find  that  they 
need  a  weaker  concave  glass,  as  in  the  case  of  a  myope 
of  •£•  or  jL.  Their  far  point  lies  at  the  distance  that  the 
presbyope's  near  point  should  be,  and  the  weaker  glass 
will  give  them  a  larger  and  more  distant  region  of 
.accommodation. 

A  still  more  interesting  case  is  the  following  : 

CASE  XL — Mr.  J.  A.,  age  50.  Although  his  glasses  have  been 
suitable  for  many  years,  he  now  finds  that,  when  reading,  the  eyes  feel 
tired  and  his  near  vision  is  not  satisfactory. 

I  find   that  the  glasses  he   is   now  wearing  are  simple 


226  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

concave  cylindrics  of  -^  in  the  horizontal  meridian. 
With  these  glasses  his  vision  is  as  follows  : 

R  E,  V  =  ft  w.  —  ^,  cyl.  ax.     70°  =  ft  J 
L  E,  V  =  H  w.  —  ,V,  cyl.  ax.  1 10°  =  f£ 

The  examination  with  the  ophthalmoscope  gives  the  same 
degree  of  refraction.  I  can  see  the  horizontal  vessels 
through  the  aperture,  being  in  the  meridian  of  greatest 
ametropia,  but  I  cannot  see  the  small  vertical  vessels 
except  with  --  2  D.  With  this  glass  all  the  vessels  un- 
cleanly seen.  We  can  then  decide  that  his  glasses  are 
correct  for  distant  vision,  but  they  do  not  suit  for  read- 
ing. Now  in  this  case  we  must  consider  what  would 
be  the  result  in  an  eye  where  the  entire  refraction  was 
the  same  in  each  of  the  principal  meridians. 

If  we  take  the  horizontal  meridian  we  find  myopia 
of  -g^,  and  at  his  age,  as  his  far  point  for  that  meridian  is 
only  20  inches,  he  would  not  require  a  glass,  while  in  the  ver- 
tical meridian  we  find  that  he  is  emmetropic.  Now,  at  fifty 
years,  the  emmetrope  will  require  a  convex  glass  of  about 
-fa  (i  .1  D).  In  this  case  this  indication  is  met  in  the  simple 
convex  cylindric  glass  of  +  -^,  and  if  we  place  this  glass 
before  his  eyes,  with  the  axis  over  the  myopic  meridiun 
at  1 80°,  or  horizontal,  we  find  that  he  can  read  No. 
i  Jaeger  at  8  inches  with  comfort.  I  would  order  this 
glass  for  reading  only,  while  he  will  continue  to  use  the 
other  glasses  for  distant  vision. 

These  cases  are  not  uncommon,  and  show  you  that 
in  astigmatic  eyes,  when  they  have  become  presbyopic, 
you  must  correct  each  meridian  just  as  an  eye  of  the 
same  degree  of  refraction. 

You  may  have  various  complications  in  the  different 
meridians,  as  I  have  shown  you  in  the  case  of  astigma- 
tism, where  the  patient,  when  young  or  under  the  age 
when  presbyopia  comes  on,  will  be  suited  with  those  glasses 


ILLUSTRATIVE    CASES,  22/ 

that  neutralize  the  exact  condition  of  refraction  which  ex- 
ists in  each  principal  meridian.  But,  when  presbyopic,  we 
must  estimate  and  treat  each  meridian  separately,  pre- 
scribing that  glass  which  will  make  the  refraction  of  each 
meridian  the  same  as  in  the  emmetropic  eye,  and  add  to 
this  the  convex  glass  that  will  restore  the  loss  in  the 
amplitude  of  the  accommodation. 

Another  very  interesting  class  of  cases  is  that  of 
amblyopia,  or  dull  vision,  in  one  eye.  This  condition  is 
generally  congenital  in  its  origin  and  then  presents  no 
evidence  of  any  pathological  process  in  the  eye.  I  will 
illustrate  it  by  the  following  : 

CASE  XII.  —  Mrs.  O.,  age  58.  She  has  worn  glasses  for  the  past 
sixteen  years,  has  changed  them  several  times,  but  the  eyes  still  give 
her  some  discomfort  with  pain  in  the  "  back  of  the  eyeballs."  She 
tells  me  that  there  is  no  vision  in  the  left  eye. 

I  find  that  the  reading  glasses  she  wears  are  for  R  E 
+  TL,  O  +  -£$,  cyl.  ax.  90°,   and  for  L  E  a  plain   glass. 
I  then  tested  her  distant  vision  and  found  it  to  be  : 


R  E,  V  =  AV,  w.  +  sV,  +  A,  cyl.  ax.  90  °  =  M  ; 

L  E,  V  =  TrJ-p-,  eccentric  vision,  improved  with  -f-  TV  to  -/-fa. 

With  this  glass  she  can  read  No.  5  Jaeger  test-type  at 
24  inches,  and  if  we  now  add  a  convex  glass  over 
the  right  eye  for  her  condition  of  presbyopia  (about 
Y1^),  and  use  the  +  ^  over  the  left  eye  to  assist  that  as 
much  as  possible,  we  then  have  this  glass  : 

R  E  +  TV,  O  +  iV>  cyl.  ax.  90°;  and 
L  E  +  TV 

With  this  glass  she  can  read  No.  i  Jaeger  at  9  inches 
easily  and  with  comfort.  I  ordered  these  glasses  for 
all  reading  and  near  work,  while  I  advised  her  to 
wear  the  glasses  that  corrected  her  compound  hyperme- 
tropic  astigmatism  for  distant  vision,  so  as  to  relieve  the 
strain  on  the  accommodation. 


228  LECTURES   ON    THE   EXKORS  OF  A'/:'/-'A'.l  C77O.Y. 

This  case  shows  :  First,  that  a  mistake  was  made  in  not 
correcting  the  refraction  of  the  amblyopic  eye  as  far  as 
possible.  Second,  that,  no  matter  how  defective  the 
vision  may  be  in  either  eye,  we  should  correct  any  error 
of  refraction,  so  that  both  eyes  may  work  together. 
Test  and  fit  each  eye  separately,  and  then  select  that 
glass  with  which  you  find  the  best  and  clearest  vision  at 
the  proper  distance.  In  the  above  case  I  heard  from 
Mrs.  O.  several  months  after  the  glasses  were  ordered, 
and  she  had  entire  relief  from  all  her  discomfort  and 
pain.  Because  the  vision  is  much  reduced  in  one  < 
from  any  cause,  we  must  not  leave  the  vision  of  that  eye 
uncorrected,  but  find  the  glass  which  will  give  the  best  and 
most  distinct  vision,  and  order  your  glasses  accordingly. 

You  will  also  meet  a  more  interesting  and  difficult  class 
of  cases  in  those  persons  who  have  astigmatic  eyes,  gen- 
erally hyperopic,  but  with  the  axis  of  the  correcting  cylin- 
dric  glass  of  the  same  meridian  in  each  eye.  I  have  already 
told  you  that  in  the  largest  number  of  cases  the  axis  of 
the  astigmatic  glass  is  at  90°  or  180°,  then  you  will  find 
them  at  45  °  in  one  eye  and  135  °  in  the  other,  or  inclining 
toward  the  nose  or  temple  in  each  eye.  But  you  will 
occasionally  meet  with  a  case  where  you  will  find  the  axis 
the  same  in  both  eyes,  say  at  45  ° — one  axis  inclining 
toward  the  nose  and  the  other  towards  the  temple.  In 
these  cases  I  would  advise  you  to  test  them  carefully  at 
their  near  and  distant  points  of  vision,  both  as  regards 
the  letters  and  the  size  and  shape  of  objects,  fitting  them 
first  for  distant  vision,  and  then  to  see  if  these  glasses  will 
also  give  perfect  vision  as  regards  letters  and  the  shape  of 
objects  at  the  near  point.  I  would  illustrate  this  to  you 
with  the  following  case,  reported  by  myself  in  the  Quar- 
terly Bulletin  of  the  New  York  Post-Graduate  School, 
vol.  ii.,  No.  3,  1887,  as  follows  : 

CASE  XIII. — Mr.  John  M.,  age  29,  consulted  me  some  six  months 


ILLUSTRATIVE   CASES.  229 

ago  in  reference  to  his  sight,  stating  that  his  vision  had  not  been  satis- 
factory for  several  years,  his  work  being  that  of  cutting  marble  and 
other  stones  in  lines  and  curves.  At  night  he  could  not  read  without 
pain  in  and  around  the  eyeballs,  though  his  eyes  did  not  pain  him 
when  at  work  in  the  daytime.  His  vision  on  testing  was  as  follows  : 

R  E,  V  =  |f,  Hm.  -gV,  reads  No.  i  Jaeger  at  7  inches  ; 

L  E,  V  =  yVo-,  accepts  no  glasses,  reads  No.  6  Jaeger  at  9  inches. 


He  thinks  the  cylindric  glasses  improve  his  vision.  On  examina- 
tion with  the  ophthalmoscope  I  find  hypermetropic  astigmatism,  with 
some  slight  myopia  in  one  meridian,  and  by  the  test  of  retinoscopy, 
decided  astigmatism  at  the  meridian  of  135°  R  E,  and  45°  L  E.  After 
using  the  solution  of  atropine  two  days  he  was  again  tested,  as  follows  : 

R  E,  V  =  |{{  —  ,  w.—  ^,  +  jV,  cyl.  ax.  45°  =  fft  +  ; 
L  E,  V  =  £fr,  w.  —  ^V,  +  uV,  cyl.  ax.  135°  =  f£ 

Then  with  the  stenopaeic  slit  at  45°  accepts  —  -^j-,  and  at  135°  with 
-j-  Jg-,  V  =  ff  in  the  right  eye  ;  and  in  the  left  eye,  with  the  steno- 
pseic  slit  at  45°  with  +  ^,  V  =  f£,  and  at  135°  with  —  ^,  V  =  -ff 
Stopping  the  atropine  solution  now  after  ten  days,  the  examination 

was  as  follows  : 

R  E,  V  =  ffc  w.  -  *V,  +  irV,  cyl.  ax.    45°    =  f*  ; 
L  E,  V  =  flfr,  w.  -  ^  +  TV,  cyl.  ax.  135°  =  f  ft. 

Testing  his  near  vision  with  this  combination,  I  find  that  in  looking 
at  square  objects,  as  a  book  or  an  envelope,  it  does  not  appear  square 
to  him  ;  that  one  side  is  much  higher  than  the  other.  I  then  found, 
by  leaving  off  the  weak  concave  glasses  and  turning  the  axes  of  the 
convex  cylindric  so  that  their  axes  would  more  nearly  correspond 
to  the  horizontal,  that  all  near  objects  would  appear  to  him  perfectly 
natural.  After  repeated  trials  with  the  convex  cylindric  glasses  I  found 
that  by  placing  over  the  R  E  +  -jV>  c>^-  ax-  20°>  and  °ver  tne  L  E  +  -$$ 
cyl.  ax.  1  60°,  he  would  have  perfect  vision  for  his  near  point,  while  the 
distant  vision  remained  at  f  %  with  the  same  glasses. 

These  glasses  were  then  ordered  for  constant  use. 
In  attempting  to  explain  the  reasons  why  we  should  be 
compelled  to  change  the  glasses  and  their  axes,  from  the 
result  of  the  examination  under  atropine,  I  am  inclined  to 
think  that  as  the  patient  looks  downwards  at  an  object 
close  to  his  near  point,  he  looks  through  the  lower  part 


230  LECTURES  ON   THE  ERRORS  OF  REFRACTION. 

or  periphery  of  the  glass,  which,  in  this  case  particularly, 
acts  as  a  prism,  and  consequently  must  change  the  rays  of 
light  as  they  pass  through  such  a  complicated  system  of 
refraction  as  takes  place  in  a  mixed  astigmatic  glass. 

The  refraction  of  the  two  principal  meridians  of  an 
astigmatic  eye  is  quite  different,  for  each  position  on  the 
meridian  of  the  cornea  that  the  rays  of  light  may  strike, 
while  the  curvature  in  any  meridian  is  different  at  its  pe- 
riphery. This  is  particularly  so  in  the  vertical  meridian  as 
the  line  of  sight  passes  through  the  glass  in  looking  up  or 
down  ;  consequently  the  rays  of  light,  as  they  pass  through 
in  the  plane  of  the  meridian,  will  focus  at  different  points. 


FIG.  89. — MEYROWITZ'  TRIAL-FRAME  FOR  GLASSES. 

Those  passing  nearest  the  optic  axis,  having  less  refraction 
than  the  rays  passing  near  the  periphery  of  the  cornea, 
will  strike  the  optic  axis  further  from  the  corneal  surface. 
This  condition  of  monochromatic  aberration  has  been 
fully  explained  by  Dr.  Swan  M.  Burnett,  of  Washington, 
D.  C.,  in  a  monograph  on  "  Refraction  in  the  Principal 
Meridians  of  a  Triaxial  Ellipsoid,"  and  in  his  "  Treatise 
on  Astigmatism,"  and,  I  am  inclined  to  think,  is  the  reason 
why  the  glasses  must  be  changed  for  the  near  point, 
together  with  the  fact  that  in  near  vision  the  patient  must 
look  through  the  periphery  of  the  correcting  astigmatic 
glass. 


ILLUSTRATIVE    CASES. 


23I 


You  will  find  this  condition  very  rare,  but  in  all  cases 
I  would  advise  you  to  test  the  vision  for  the  near  point 
before  you  order  astigmatic  glasses,  when  the  axes  are  at 
any  other  point  than  that  of  90°  or  180°,  and  particularly 
so  when  you  find  the  axes  of  each  eye  the  same. 

Another  class  of  cases  you  will  meet  with  are  those 
in  which  the  condition  of  anisometropia  exists — that  is,  a 
difference  in  the  refraction  of  each  eye — when  the  question 
arises,  Shall  we  fit  each  eye  separately,  giving  full  correc- 
tion for  each  degree  of  refraction  existing  in  the  examined 
eye  ?  The  answer  to  that  would  be,  that  it  depends  upon 
the  degree  and  kind  of-refraction  and  upon  the  difference 
between  the  degrees.  This  has  been  partially  illustrated 
in  the  case  in  which  one  of  the  eyes  was  amblyopic  ;  but 
under  the  present  class  of  cases,  where  the  vision  of  each 
eye,  with  a  suitable  glass  is  perfect,  as  J--JJ-,  you  must  now 
consider  the  size  of  the  retinal  image,  and  endeavor  to 
have  the  eyes  work  in  unison.  Let  me  illustrate  this  to 
you  with  the  following  interesting  case  : 

CASE  XIV. — Miss  J.  C,  age  15,  now  at  school.  When  studying 
for  any  length  of  time,  as  for  half  an  hour,  she  has  headache  and 
"  pain  across  the  eyes,"  with  blurring  of  the  vision  when  reading 
music. 

On  examination  at  first,  I  found  as  follows  : 

R  E,  V  =  f£,  Hm.  -s-V  ; 
L  E,  V  =  ffc  Hm.  3V 

She  reads  No.  i  Jaeger  test-type  at  6  inches  ;  retinoscopy 
and  the  ophthalmoscope  show  mixed  astigmatism. 
After  using  atropine  the  result  was  : 

R  E,  V  =  ,%,  w.  -  «V,  C  +  rir,  cyl.  ax.    80°    =  fft  —  ; 
L  E,  V  =  -gVo,  w.  —  &,  C  +    i,  cyl.  ax.  100°  -  f#  — . 

When  examined  ten  days  after  the  atropine  had  been 
discontinued,  the  vision  was  : 


232  LECTURES  ON  Till:    l-.RRORS  OF  REFRACTION. 

R  E,  V  =  f|,  w.  +  A,  cyl.  ax.  75  -  =  ff  ; 

L  E,  V  =  |8,  w.  —  &,  C  +  A  cyl.  ax.  105  °  =  H- 

And  with  this  glass  she  can  read  No.  i  Jaeger  test-type 
at  from  5  to  8  inches.  These  glasses  were  ordered  for 
constant  use. 

You  will  see  that  in  this  case  each  eye  was  fitted 
entirely  independent  of  the  other,  and  when  the  glasses 
were  used  vision  was  very  satisfactory.  But  you  will  find 
in  many  cases  that  you  cannot  fit  each  eye  perfectly,  as  one 
eye  may  be  emmetropic,  myopic,  or  hypermetropic,  and 
the  other  different  in  degree  or  variety  of  refraction,  even 
so  far  that  one  eye  will  be  myopic'  and  the  other  hyper- 
metropic ;  therefore  first  decide  what  is  the  total  degree 
of  ametropia  in  each  eye,  and  then  see  if  they  can  work 
together  with  the  correcting  glasses. 

I  would  advise  you  to  follow  two  simple  rules,  as  far 
as  possible,  and  these  are  :  First  correct  all  the  degrees 
of  astigmatism  that  may  be  in  each  eye  separately,  and 
then  add  the  necessary  spherical  glass.  Second,  correct 
the  least  ametropic  eye,  and  then  fit  the  other  with  a 
glass  as  near  to  that  as  will  give  the  best  vision.  This 
rule  will  also  apply  to  eyes  that  are  not  astigmatic.  For 
instance,  if  you  have  a  high  degree  of  myopia  in  one  and 
a  medium  or  low  degree  in  the  other,  you  can  fit  the  eye 
with  the  least  myopia  first,  and  then  order  a  glass  some- 
what stronger,  not  to  full  correction,  for  the  other  eye. 

The  rule  is  that  you  should  not  have  more  than  a 
difference  of  i  D  between  the  glasses,  and  I  would  recom- 
mend you  to  make  repeated  tests  with  the  glasses  in  the 
trial  frame,  and  then  decide  which  glass  will  give  the  most 
comfort. 


SN  ELLEN'S    TEST-TYPES. 


D  =  0,5. 


The  Gallic  tribes  fell  off,  and  sued  for  peace.  Even 
the  Batavians  became  weary  of  the  hopeless  contest, 
•while  fortune,  after  much  capricious  hovering,  settled 
at  last  upon  the  Roman  side.  Had  Civilis  been  suc- 
cessful, he  would  have  been  deified;  but  his  misfortune's, 
at  last,  made  him  odious  in  spite  of  his  heroism.  But 


the  Batavlan  wag  not  a  man  to  be  crashed,  nor  had 
he  lired  so  long  In  the  Roman  service  to  be  out- 
matched in  politics  by  the  barbarous  Germans. 
He  was  not  to  be  sacrificed  as  a  peace-offering  to 
revengeful  Rome.  Watching  from  beyond  the  Rhine 
the  progress  of  defection  and  the  decay  of  national 


D  =  0,6. 


enthusiasm,  he  determined  to  be  beforehand  with  those  who  were  now  his  enemies.  He 
accepted  the  offer  of  negotiation  from  Cerialis.  The  Roman  general  was  eager  to  grant  a 
full  pardon,  and  to  re-enlist  so  brave  a  soldier  in  the  service  of  the  empire.  A  colloquy  was 
agreed  upon.  The  bridge  across  the  Nabalia  was  broken  asunder  in  the  middle,  and  Cerialis 
and  Civilis  met  upon  the  severed  sides.  The  placid  stream  by  which  Roman  enterprise  had 
connected  the  waters  of  the  Rhine  with  the  lake  of  Plevo,  Bowed  between  the  imperial 


D  =  0,8. 

•commander  and  the  rebel  chieftain.  —  Here  the  story  abruptly  terminates. 
The  remainder  of  the  Roman's  narrative  is  lost,  and  upon  that  broken  bridge 
the  form  of  the  Batavian  hero  disappears  for  ever.  His  name  fades  from 
history;  not  a  syllable  is  known  of  his  subsequent  career;  everything  is 
buried  in  the  profound  oblivion  which  now  steals  over  the  scene  where  he 
was  the  most  imposing  actor.  The  contest  of  Civilis  with  Rome  contains  a 

D  =  1 


remarkable  foreshadowing  of  the  future  conflict  with  Spain,  through 
which  the  Batavian  republic,  fifteen  centuries  later,  was  to  be 
founded.  The  characters,  the  events,  the  amphibious  battles,  despe- 
rate sieges,  slippery  alliances,  the  traits  of  generosity,  audacity, 
and  cruelty,  the  generous  confidence,  the  broken  faith,  seem  so 
closely  to  repeat  themselves,  that  history  appears  to  present  the 

D  =  1,25. 


selfsame  drama  played  over  and  over  again,  with  but 
a  change  of  actors  and  of  costume.  There  is  more  than 
a  fanciful  resemblance  between  Civilis  and  William  the 
Silent,  two  heroes  of  ancient  German  stock,  who  had 
learned  the  arts  of  war  and  peace  in  the  service  of  a 
foreign  and  haughty  world-empire.  Determination, 

•233 


234 


SNELLEN'S    TEST-TYPES. 
200  feet  or  6om. 


100  feet  or  3om. 


V  =  rffr  or  f 

The  numbers  above  the  letters  indicate  the  distance,  in  feel  and  metres,  at  which 
they  are  seen  under  an  angle  of  five  minutes  ;  those  below  each  series  of  letter--  ex- 
press the  amount  of  vision  which  a  patient  has  that  can  recognize  such  types  only  at 
a  distance  of  twenty  feet  from  the  eye. 


SNELLEWS   TEST-TYPES. 
80  feet  or  24m. 


235 


V  =  f§  or 
60  feet  or  i 


V  =  f g  or  =  -' . 
50  feet  or  I5m. 


40  feet  or  I2m. 


FDTC 


V  =  f  %  or  =  *, 
30  feet  or  gm. 


V  =    |o    or  |. 

20  feet  or  6m. 


U  O  F  L  P  H  E 


V  =.  4ft  or  =  L 


INDEX. 


Absolute  hypermetropia,  64 

Accommodation,  spasm  of,  76 

Accommodative,  movements,  10 ;  myopia,  76 

Acuteness,  visual,  44 

Amaurosis,  79 

Amblyopia,  79 

Amblyopic  eye,  63 

Ametropic  eye,  57 

Anatomy  of  the  eye,  i 

Angle,  of  incidence,  22  ;  of  refraction,  22  ;  of  refraction  in  the  eye,  34 ; 
visual,  48 

Angle  "a,"  123  ;  estimation  of,  125 

Anisometropia,  205 

Anterior  pole  of  the  eye,  6 

Apparent  myopia,  76 

Arteria  centralis  retinae,  6 

Artery,  ophthalmic,  6  ;  ciliary,  6 

Associated  movements,  10 

Asthenopia,  muscular,  113  ;  illustrative  case  of,  209 

Astigmatism,  144  ;  from  curvature  of  cornea,  153  ;  causes  of,  144  ; 
compound,  156  ;  concealed,  158  ;  diagnosis  with  ophthalmoscope, 
89,  165  ;  diagnosis  with  retinoscopy,  191  ;  hypermetropic,  154, 
156  ;  hypermetropic  compound,  154,  157  ;  irregular,  147  ;  irregu- 
lar, diagnosis  of,  147  ;  irregular,  to  correct,  146  ;  myopic,  154, 
156  ;  myopic,  compound,  154,  157  ;  mixed,  154,  157  ;  position  of 
meridians,  154  ;  regular,  150  ;  simple,  155 

Axes,  of  rotation,  n,  114  ;  secondary,  16,  28 

Axial,  hypermetropia,  58  ;  myopia,  69 

Axis,  optic,  6  ;  vertical,  in  astigmatism,  114  ;  horizontal,  in  astigma- 
tism, 114  ;  visual,  6 

Black  drop,  explanation  of,  147 
Blind  spot,  53 
Bonnet's  capsule,  5 

237 


238  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

Canal  of  Petit,  16 

Centre,  of  rotation,  10  ;  optical,  29 

Ciliary  artery,  6  ;  muscle,  1 2 

Clonic  spasm,  76 

Compound  lenses,  150 

Concavo-convex  lens,  24,  32 

Conical  cornea,  148  ;  diagnosis  of,  148 

Conjugate  foci,  45,  81 

Convergence,  maximum,  140  ;   minimum,  141  ;   negative  part  of,  55, 

140  ;  positive  part  of,  140 
Cornea,  15  ;  conical,  148 
Crossed  diplopia,  1 2 1 
Crystalline  lens,  16 
Cylindrical  lens,  36  ;  axis  of,  36 

Decentred  glasses,  141 

Deviation,  primary,  63  ;  secondary,  64 

Diagnosis  of  astigmatism,  with  ophthalmoscope,  89,  165  ;  with  retino- 

scopy,  191 

Dioptric,  media,  19  ;  system,  39 
Diplopia,  120;   homonymous,   120;   crossed,   121;   monocular,   130; 

test  at  near  point,  128 

Ellipsoid,  triaxial,  145 

Emerson's  perimeter,  52 

Emmetropia,  43  ;  diagnosis  with  ophthalmoscope,  80  ;  glasses  for,  56 

Emmetropic  eye,  44 

Equator  of  the  eye,  6 

Equatorial  plane,  6 

Facultative  hypermetropia,  61 

Field  of  vision,  54  ;  quantitative,  51  ;  qualitative,  51 

Foci,  conjugate,  45,  81 

Fovea  centralis,  1 7 

Glasses,  for  emmetropia,  56  ;  decentred,  141  ;  for  hypermetropia,  66  ; 

for  myopia,  73 
Green's  test-card  for  astigmatism,  162 

Hemianopsia,  55 
Hemiopia,  55 

Homonymous  diplopia,  120 
Horizontal  axis  in  astigmatism,  114 


INDEX.  239 

Hypermetropia,  57  ;  absolute,  64  ;  absolute  manifest,  64  ;  axial,  58  ; 
concealed,  61  ;  facultative,  61  ;  glasses  for,  66  ;  latent,  61  ;  mani- 
fest, 59  ;  by  ophthalmoscopy,  87  ;  by  retinoscopy,  185  ;  refractive, 
58  ;  relative,  62  ;  total,  61 

Hyperopia,  57 

Illustrative  cases,  absence  of  accommodation,  220 ;  anisometropia,  229  ; 
astigmatism,  227  ;  amblyopia,  227  ;  emmetropia,  209  ;  hyperme- 
tropia,  210  ;  myopia,  211  ;  myopic  astigmatism,  212  ;  paresis  of 
accommodation,  219  ;  presbyopia,  225  ;  presbyopia  with  astigma- 
tism, 227  ;  spasm  of  accommodation,  217 

Inch  system,  39 

Incidence,  angle  of,  22 

Index  of  refraction,  22 

Insufficiency  of  muscles,  119 

Interval  of  Sturm,  150 

Iris,  35 

Javel's  test-card  for  astigmatism,  163 
Keratoscope,  Placido's,  148 

Latent  hypermetropia,  61 

Lens,  cylindrical,  36  ;  crystalline,  16  ;  negative,  31  ;  positive,  27 

Lenses,  23  ;   bi-convex,  23,  27  ;   bi-concave,  23,  31  ;   concavo-convex, 

24,  32  ;  plano-convex,  23  ;  plano-concave,  23  ;  meniscus,  23,  32 
Limit  angle,  21 

Macula  lutea,  17 

Manifest  hypermetropia,  59 

Mariotte's  blind  spot,  54 

Meridians  of  the  eye,  36 

Metric  system,  39  ;  table  of,  41 

Movements  of  the  eye,  115 

Muscle,  ciliary,  1 2  ;  oblique  superior,  9  ;  oblique  inferior,  9  ;  recti,  8  ; 

to  test  the  power  of,  136 
Muscular  asthenopia,  113 
Myopia,  68  ;  accommodative,  76  ;   apparent,  76  ;  axial,  69  ;  causes  of, 

70  ;    glasses  for,  73  ;   high  degrees,  75  ;   by  ophthalmoscopy,  88  ; 

progressive,  69  ;  by  retinoscopy,  152  ;  refractive,  69  ;  vision  of,  71 

Negative,  convergence,  140  ;  lens,  31 

Nerve,  fourth,  7  ;  sixth,  7  ;  third,  7  ;  ciliary,  8 


240  LECTURES  ON  THE  ERRORS  OF  REFRACTION. 

Nerves  of  the  eye,  6 
Nodal  point,  6 
Normal  eye,  44 

Ophthalmic  artery,  6 

Optical  centre,  29 

Optic  axis,  6 

Optic  foramen,  3 

Ophthalmoplegia,  externa,  134 

Ophthalmoscope,  Valk's,  83  ;  description  of,  84  ;  distance  to  use,  107  ; 

indirect  method,   Hartridge,   108 ;   practice  in  the  use  of,  112; 

theory  of  the,  85 
Ophthalmoscopy,  79  ;    for  hypermetropia,  87  ;    for  myopia,  88  ;    for 

emmetropia,  86  ;  for  astigmatism,  89  ;  examiner  may  be  ametropic, 

104  ;  theory,  101 
Ophthalmo-dynamometer,  Landolt's,  138 

Paralyses,  table  of,  133 

Paralysis  of  muscles,  115,  117 

Paresis,  of  muscles,  115 

Petit,  canal  of,  16 

Perimeter,  52  ;  Emerson's,  52 

Periodic  squint,  or  strabismus,  62,  126 

Placido's  Keratoscope,  148 

Planes  of  the  eye,  36 

Presbyopia,  195  ;   on  what  it  depends,  197  ;    to  test  for,  199  ;   with 

astigmatism,  202  ;  with  hypermetropia,  200  ;  with  myopia,  201 
Primary  position,  of  the  eyes,  113  ;  deviation,  63 

Prisms,  principal  angle,  131  ;  angle  of  deviation,  131  ;  how  to  order,  141 
Progressive  myopia,  69 
Projection  of  image,  128 
Posterior  pole  of  eye,  6 

Punctum,  ccecum,  54  ;  remotum,  65  ;  remotum  negative,  65 
Pupilloscopy,  75 

Qualitative  field,  51 
Quantitative  field,  51 

Refraction,  18  ;  angle  of,  22  ;  at  periphery  of  lens,  143  ;  index  of,  22  ; 

of  the  eye,  14  ;  of  a  prism,  25  ;  of  a  convex  lens,  27  ;  of  a  concave 

lens,  31 

Refractive  hypermetropia,  58 
Relative  hypermetropia,  62 


INDEX.  241 

Retina,  16 

Retinal  image,  to  estimate  size,  46 

Retinoscopy,  175  ;  in  myopia,  182  ;  in  emmetropia,  190  ;  in  astig- 
matism, 191  ;  in  hypermetropia,  185  ;  with  concave  mirror,  176  ; 
with  plane  mirror,  178  ;  theory  of  shadow,  180 

Rotation,  centre  of,  10  ;  axes  of,  n 

Secondary,  axes,  28  ;  position,  113  ;  deviation,  64 

Second  sight,  204 

Shadow  test,  175 

Snellen's  test-type,  47 

Spasm,  of  accommodation,  76  ;    clonic,  76  ;    diagnosis  of,  78  ;    tonic, 

76  ;  treatment  of,  78 

Squint,  62  ;  periodic,  126  ;  apparent,  123 
Stenopaeic  slit,  164 
Strabismus,  62;    angle  of,  118  ;    causes  of,  117;     convergens,  130; 

convergent  concomitant,  116  ;    divergens,  130;    divergent,   130; 

fixed,  63,  116  ;  periodic,  62  ;  permanent,  63,  116  ;  to  detect,  117 

Tenon's  capsule,  4 
Tonic  spasm,  76 
Total  hypermetropia,  61 
Trial  cases,  38 
Triaxial  ellipsoid,  145 

Vertical  axis,  in  astigmatism,  114 
Vision,  field  of,  51  ;  to  record,  51 
Visual  axis,  6  ;  acuteness,  44  ;  angle,  48 
Vitreous  body,  16 

Yellow  spot,  17 
Zone  of  Zinn,  15 

THE   END. 


UNIVERSITY  OF  CALIFORNIA  LIBR  \K\ 
Los  Angrlcs 

This  book  is  DUE  on  the  last  date  stamped  below. 


Form  L9-Series  4939 


